UC-NRLF 


UNITED  STATES  NOETHERN  BOUNDARY  COMMISSION. 


DECLINATIONS  OF  FIXED  STARS. 


BY 


LEWIS    BOSS, 

<\ 

NOW  DIRECTOR  OF  DUDLEY  OBSERVATORY. 


.'o\S 


'  «l 

*  f    *.  r       *  x 


REPORT 

ON 

THE  DECLINATIONS  OF  THE  STARS  EMPLOYED  IN  LATITUDE  WORK  WITH 
THE  ZENITH  TELESCOPE,  EMBRACING  SYSTEMATIC  CORRECTIONS  IN  DE- 
CLINATION DEDUCED  FOR  VARIOUS  AUTHORITIES,  AND  A  CATALOGUE  OF 
FIVE  HUNDRED  STARS  FOR  THE  MEAN  EPOCH  1875, 

BY 

ASSISTANT  LEWIS  BOSS, 

NOW  DIRECTOE  OF  DUDLEY  OBSERVATORY. 


DUDLEY  OBSERVATOBY, 
Albany,  N.  T.,  February  21, 1877. 

DEAK  SIR:  After  unexpected  delay  I  Lave  the  honor  to  transmit,  herewith,  my 
report  ou  the  accuracy  of  the  declinations  adopted  by  the  United  States  Commission 
in  the  latitude  work  ol'  the  Northern  Boundary  Survey.  In  doing  this,  permit  me  to 
thank  you  most  cordially  for  the  kind  interest  and  generous  support  which  you  have 
throughout  accorded  to  this  undertaking.  The  sense  of  obligation  is  the  more  keenly 
felt,  when  I  reflect  upon  the  many  imperfections  and  deficiencies  of  the  work;  but 
your  intercourse  with  me  has  been  uniformly  such  as  to  cause  me  to  forget  the  debt, 
and  leaves  only  the  most  pleasant  recollections. 

I  have  the  honor  to  be,  very  respectfully,  your  obedient  servant, 

LEWIS  BOSS, 

Director  of  Dudley  Observatory,  and  late  Assistant 
Astronomer  of  the  United  States  Northern  Boundary  Commission. 
Capt.  WILLIAM  J.  TWINING, 

United  States  Engineers,  Chief  Astronomer  and 

Surveyor  of  the  United  States  Northern  Boundary  Commission. 


INTRODUCTORY. 

The  method  of  obtaining  latitudes  with  the  zenith  telescope,  which  was  adopted 
by  the  United  States  Northern  Boundary  Commission,  rendered  it  necessary,  in  1872, 
to  calculate  the  declinations  of  a  large  number  of  stars.  The  short  time  allowed  lor 
preparation  rendered  a  critical  discussion  of  these  star-places  quite  impracticable. 
The  declinations  adopted  in  the  work  of  1872  were,  therefore,  derived  from  a  limited 
number  of  authorities;  but  were  subsequently  revised  whenever  additional  material 

409 


340729 


410          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.  [4] 

could  be  secured.  Thus  the  catalogue  for  1874  was  compiled  from  nearly  all  the 
authorities  which  could  be  obtained  from  the  library  of  the  United  States  Naval 
Observatory. 

The  method  of  reduction  was  substantially  that  employed  by  Argelander  in  the 
seventh  volume  of  Bonn  observations.*  The  principal  deviations  from  this  plan  con- 
sisted in  the  smaller  weights  given  to  declinations  from  the  older  authorities,  and  in 
applying  no  systematic  corrections  to  those -of  a  mean  date  later  than  1860. 

Upon  the  accuracy  of  the  adopted  declinations  depend  the  latitudes  of  twenty-two 
stations  in  the  vicinity  of  the  forty-ninth  parallel.  There  is  every  reason  to  believe 
that  for  the  majority  of  the  stations  the  error  in  location  due  to  instrumental  causes 
is  practically  insignificant,  and  that  if  any  considerable  correction  is  needed  it  may 
sateiy  be  ascribed  to  systematic  error  in  the  values  of  declination  assigned  to  the 
determining  stars. 

To  ascertain  the  numerical  limits  between  which  the  value  of  such  a  correction  is 
likely  to  exist,  and,  as  far  as  practicable,  to  compute  its  actual  amount,  was  the  original 
purpose  of  this  discussion. 

When  the  work  was  about  half  completed,  it  appeared  that  the  systematic  correc- 
tions and  the  declinations  of  the  principal  stars,  adopted  as  standard  in  this  paper, 
might  prove  acceptable  to  others  engaged  in  certain  classes  of  astronomical  reductions. 
This  circumstance  led  to  a  considerable  enlargement  of  the  original  scope  of  the  work. 
Only  stars  of  the  northern  hemisphere,  with  a  few  in  the  first  ten  degrees  of  south 
declination,  had  hitherto  been  considered.  The  list  was  uowextended  so  as  to  include 
all  the  stars  of  the  American  Ephemeris. 

Quite  recently,  upon  my  appointment  to  the  astronomical  direction  of  Dudley 
Observatory,  the  work  received  an  additional  impulse  from  my  determination,  in 
reducing  observations  made  with  the  transit  circle,  to  use  a  standard  catalogue  in 
declination  as  well  as  right  ascension.  This  course  was  adopted  for  the  reason  that, 
whenever  the  places  of  the  principal  fixed  stars  can  be  predicted  from  observations 
already  made,  with  greater  accuracy  than  they  can  be  determined  at  any  one  observa- 
tory by  a  single  series  of  a  few  years  duration,  a  desire  for  the  greatest  economy  of 
labor  and  accuracy  in  results  should  dictate  one  of  two  courses :  either  a  special  and 
rigorous  research,  having  in  view  the  independent  determination  of  the  places  of  a 
small  number  of  the  brighter  stars;  or,  the  use  of  a  standard  catalogue,  compiled  from 
the  best  available  sources,  to  which  the  observations  of  all  other  objects  should  be 
essentially  referred. 

It  is  much  to  be  regretted  that  owing  to  unavoidable  circumstances  this  change  in 
plan  was  made  too  late  for  the  most  advantageous  disposition  of  materials  available 
for  the  purpose  in  view.  On  the  other  hand,  the  corrections  and  the  resulting  declin- 
ations are  probably  very  near  those  which  would  have  resulted  from  a  more  systematic 
and  elaborate  discussion,  adopting  the  same  general  principles. 

This  considerable  extension  of  the  original  plan  was  determined  upon  at  a  time 
when  it  was  out  of  the  question  that  the  computations  should  be  completed  during 
the  existence  of  the  boundary  commission;  so  that  in  the  performance  of  the  work  it 
has  been  necessary  for  me  to  incur  many  obligations.  For  material  assistance  I  am 
especially  indebted  to  Prof.  Simon  Newcomb,  of  the  United  States  Naval  Observatory. 

*  Bonn  Seob.,  Band  VII.,  Abth.  I.,  "  Untersuchungeu  iibur  tiic  Eigenbewegungen  von  200  Sternen." 


[5]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          41 1 

Without  bis  generous  intervention  it  would  have  been  impossible  for  me  to  Lave  com- 
pleted the  work  in  its  present  extent,  within  the  prescribed  limits  of  time,  For  further 
aid,  I  am  under  the  greatest  obligations  to  the  office  of  the  American  Ephemcris  and 
Nautical  Almanac ;  and  to  the  Dudley  Observatory,  where  the  later  computations  have 
been  carried  on  partly  for  the  purpose  of  constructing  a  standard  catalogue  of  declin- 
ations, for  use  with  the  transit  circle,  as  already  explained. 

The  services  of  several  computers  have  been  engaged  from  time  to  time,  generally 
for  short  periods.  For  such  services,  I  am  chiefly  indebted  to  Assistant  C.  L.  Doolittle, 
since  Professor  of  Mathematics  and  Astronomy  in  the  Lehigh  University,  Pennsylvania, 
and  to  Assistant  O.  S.Wilson,  who  have  labored  on  the  work  in  a  most  disinterested 
and  competent  manner.  My  thanks  are  also  due  to  Thomas  R.  Featherstouhangh, 
A.  M.,  formerly  assistant  at  the  Dudley  Observatory. 

The  facilities  of  the  Observatory  at  Washington  were  most  kindly  extended  to  me 
by  Admiral  B.  F.  Sands,  Superintendent,  and  by  his  successor  in  office,  Admiral  C.  H. 
Davis.  To  the  various  members  of  the  astronomical  corps  at  that  institution  I  desire 
to  express  my  acknowledgments;  particularly  to  Professors  Eastman,  Harkness,  and 
Nourse,  for  special  courtesies. 

PEELIMINAEY  STATEMENT  AND  GENERAL  PLAN  OF  THE  WORK. 

It  is  well  known  that  troublesome  systematic  discordances  exist  even  among  inde- 
pendent declination  determinations  of  the  highest  rank,  while  the  differences  which 
were  found  between  the  earlier  results  of  Bessel,  Brinkley,  and  Pond,  and  even  between 
different  results  by  the  same  astronomer,  were  such  as  to  provoke  an  acrimonious  con 
troversy  and  to  lead  to  most  erroneous  theories.  The  science  of  exact  measurement  of 
zenith  distances  was  no  doubt  very  much  stimulated  by  the  latter  circumstances,  for  in 
the  period  extending  from  1820  to  1850  we  have  more  than  one-half  the  entire  material 
now  available  for  researches  upon  the  absolute  declinations  of  the  fundamental  stars. 

For  the  purpose  here  proposed,  it  will  not  be  necessary  to  make  any  extensive 
enumeration  of  the  attempts  which  have  been  made  from  time  to  time  to  ascertain  and 
reconcile  these  differences.  Since  the  appearance  of  Bessel's  reduction  of  Bradley's 
observations,*  the  uniform  practice  has  been  to  consider  these  places  for  1755  as  abso- 
lute, and  to  compare  them  with  the  results  of  a  single  modern  series,  or  with  the  mean 
of  two  or  more.  With  the  declinations  and  proper  motions  thus  formed,  the  corrections 
necessary  to  reduce  any  given  series  to  the  standard  could  be  ascertained.  Miidler 
compared  a  number  of  modern  catalogues  with  Pond's  Catalogue  of  1,112  stars,  the 
proper  motions  being  derived  from  the  Fundamental  Dr.  Gould  reduced  the  star- 
places  now  adopted  in  the  American  Ephemeris  in  a  similar  manner,  using  for  the 
modern  catalogue  the  Abo  Catalogue  of  the  late  Dr.  Argelander.f  Dr.  Wolfers  cor- 
rected the  declinations  of  Bessel's  Tdbulce  Regiomontancc,  using  for  that  purpose  eleven 
modern  catalogues.  Many  series  of  observations  were  adapted  to  the  system  thus 
formed  through  the  labors  of  Dr.  Argelauder  and  Dr.  Auwers.§  The  latter  has  con- 

*  Fundamenta  Astronomiai  pro  anno  1755,  ex  obtervationibua  J.  Bradley,  Aitctore  F.  \V.  Bessel.  Begio- 
monti,  1818. 

tDorpat  observations,  vol.  xiv.    J.  II.  MUdler. 

t  Dr.  B.  A.  Gould's  Standard  Watts  of  Fundamental  Stars,  Untied  Stales  Coast  Survey,  18GC. 

$  Tabulce  Ileductionum,  Auctore  J.  Pb.  Wolfers.  Berollni,  1858.  Dr.  Auwers  in  Astronomische  Xachrich- 
ten.  Dr.  Argelander,  Astroitomische  Nachrichten,  Bonn  liiob.  lid.  vii,  etc. 


412          UNITED  STATES  NORTHERN   BOUNDARY  COMMISSION.  [6] 

tributed  an  exhaustive  independent  investigation  of  declination  corrections  in  Astro- 
nomisclie  Nachrichten,  Baud  04  (pp.  305  to  382).  Taking  the  Abo  Catalogue,  referred  to 
the  Fundamenta^,  as  the  medium  of  comparison,  the  corrections  necessary  to  reduce  the 
principal  modern  series  of  observed  declinations  to  the  system  of  the  Abo  are  first 
ascertained  and  afterward  corrected  by  the  mean  of  fourteen  catalogues  judged  most 
suitable  for  the  purpose,  in  such  a,  way  that,  for  the  epoch  1755,  the  system  is  that  of 
the  Fundamenta  as  at  first  ;  but  for  the  mean  modern  date  (about  1837)  that  of  the  mean 
of  the  fourteen  catalogues.  •  Shortly  afterward  (A.  N.,  Bd.  64,  p.  193)  Dr.  Auwers  used 
these  corrections  in  discussing  the  declinations  of  thirty-four  fundamental  and  nine 
circumpolar  stars.  Similar  discussions  and  compilations  relating  to  star  declinations 
have  also  been  made  by  Baily,*  Laugier,t  Safford,f  Bruhns,§  and  others. 

It  is  evident  in  the  cases  cited  that,  it'  we  denote  by  J  N  the  correction  required 
by  n  normal  system  for  the  epoch  T,  which  corresponds  to  the  mean  of  the  modern 
catalogues  employed  in  its  formation,  and  by  A  B  the  correction  required  for  the  same 
system  —  or  what  is  the  same  thing,  Bessel's  Fundamenta  —  at  the  epoch  1755,  the  cor- 
rection of  the  system  for  any  other  epoch  T'  will  be, 


If  we  put  AN=G  and  T=1835,  wo  shall  have  as  the  correction  of  the  normal 
system,  when  T1  =  1875, 

-\AB. 

Thus,  if  declinations  are  required  for  the  epoch  1875,  a  single  determination  at  that 
date  having  weight  5,  when  the  unit  of  weight  is  the  corresponding  determination  by 
Bradley,  is  worthy  of  more  confidence  than  that  which  is  derived  from  a  discussion 
which  assumes  the  Fundamenta  as  absolute  at  the  epoch  1755,  even  though  modern 
determinations  be  absolutely  without  error  for  the  epoch  1835. 

After  the  time  of  Bradley  we  meet  with  uo  important  independent  determination 
of  declination  until  that  of  Piazzi  for  the  mean  epoch  1800.  But  the  instrument  used 
in  this  series  was  entirely  inadequate  for  the  purpose,  and  although  all  the  elements  of 
reduction  —  precession,  nutation,  and  aberration  (-xcepted  —  were  derived  from  the  obser- 
vations themselves,  the  execution  of  the  work  is  not  such  as  to  command  our  entire 
confidence.  Passing  over  the  circumpolar  catalogue  of  Groombridge  (epoch  1810),  the 
first  which  appears  to  answer  our  requirements  results  from  observations  made  with 
the  Eeicheubach  circle,  in  1820  and  1821,  by  Bessel  (Eonigslerg  Beob.,  vol.  vii).  This 
may  be  regarded  as  the  first  example  in  the  new  era  of  declination  determinations  with 
meridian  instruments.  The  form  of  discussion  there  employed  has,  with  slight  modifi- 
cations, served  as  a  model  for  similar  independent  researches  of  I  he  highest  order  ever 
since  that  time;  and  since  this  epoch  there  is  no  lack  of  material  for  the  formation  of 
standard  catalogues  of  declination. 

*  Catalogue  of  the  Royal  Astronomical  Society  for  1830.  British  Association  Catalogue  of  8,377 
stars  for  the  epoch  1850,  etc. 

t  Memoire  sur  la  Determination  da  Distances  Polaires  dcs  Eloiks  Fondamcntales  par  E.  Laugicr.  Deux- 
ibme  section,  p.  75. 

t  Annals  of  Harvard  College  Ohservatory  ;  Memoirs  American  Academy,  New  Series,  vol.  iii  ;  Mean 
dcclinatious  .of  981  stars  for  1875,  Washington,  1873,  etc. 

$  Gencralbcrichl  dcr  Eitropaisclien  Gradmessung,  1«71. 


[7]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  413 

It  will  be  shown  tbat  the  interval  of  time  between  the  group  of  early  determina- 
tions by  Bessel  (1821),  Struve  (1824),  and  Argelander  (1829),  and  the  later  ones  at 
Leiden,  Melbourne,  Greenwich,  and  Washington  observatories  (not  to  mention  inter- 
mediate catalogues),  is  quite  sufficient  for  an  independent  judgment  as  to  the  approxi- 
mate accuracy  and  consequent  weight  of  Bradley's  results,  and  that  a  reliable  system 
of  corrections  to  the  various  catalogues  may  be  founded  on  a  discussion  of  recent  cata- 
logues alone,  taking  as  the  earliest  that  of  Bessel  for  the  mean  epoch  1821. 

Having  premised  this  much,  for  the  purpose  of  a  more  exact  understanding  of  the 
scope  and  contents  of  the  succeeding  pages,  the  successive  steps  and  objective  points 
will  be  indicated  in  brief.  These  are: — 

1.  The  selection  of  stars  to  form  the  catalogue,  and  particularly  of  a  list  of  stars 
most  frequently  observed,  which  shall  serve  as  the  basis  of  the  normal  system  and  as 
a  medium  of  comparison  between  the  various  series  of  observations. 

2.  The  formation  of  approximate  positions  and  proper  motions  for  the  fictitious 
epoch  1875.0.    These  will  be  necessary  for  the  computation  of  precession  coefficients. 
Furthermore,  the  values  of  the  assumed  d  and  /j.'  should  be  fair  approximations,  for 
reasons  which  will  appear  in  the  proper  place. 

3.  The  computation  of  precession  coefficients,  and  with  the  aid  of  these  (and  in  the 
case  of  close  circumpolar  stars  by  the  rigorous  formula)  the  reduction  of  the  individual 
declinations  to  the  required  epochs,  in  order  that  the  assumed  declinations  may  be  cor- 
rected by  comparison  with  the  observed  values. 

4.  The  selection  of  catalogues  and  series  of  observations,  which  shall  serve  in 
various  stages  of  the  work  to  correct  the  assumed  declinations.    These  will  be  divided 
into  three  classes. 

5.  The  application  to  the  declinations  given  by  these  catalogues  of  certain  correc- 
tions deemed  advisable  from  an  inspection  of  the  constants  and  methods  of  reduction, 
and  numerous  compilations  of  the  results  of  several  successive  years  at  the  same  obser- 
vatory into  single  catalogues  embracing  convenient  intervals  of  time.    These  correc- 
tions are  such  as  can  be  determined  without  recourse  to  comparisons  of  the  determina- 
tions of  one  instrument  with  those  of  another.    The  compilations  are  for  the  purpose 
of  rendering  available  a  large  mass  of  material  that  would  otherwise  be  inconvenient 
or  unsuitable  for  the  purpose  here  proposed.    Generally,  published  catalogues,  which 
combine  in  one  determination  the  results  of  several  years,  have  been  used  without 
change. 

6.  The  collection  of  results  and  formation  of  the  approximate  normal  system  from 
a  discussion  of  the  declinations  of  the  fundamental  and  principal  circumpolar  stars, 
using  for  this  purpose  only  those  series  of  observations  which  are  supposed  to  give 
determinations  of  sufficient  independence  and  weight. 

7.  By  the  aid  of  the  approximate  corrections  to  the  selected  list  of  authorities  to 
enlarge  the  number  of  standard  declinations,  and,  in  turn,  with  these  to  derive  the 
systematic  correction  required  by  Bradley's  observations  as  reduced  by  Bessel  in  the 
Fundamenia  Astronomies. 

8.  With  this  correction  together  with  those  previously  found,  and  with  an  increased 
list  of  stars,  to  ascertain  corrections  to  the  assumed  declination  and  proper  motion  of 
each  star;  and  taking  them  as  a  basis,  to  compute  definitive  corrections  and  weights 
for  all  the  catalogues  except  those  of  the  third  class;  with  which  final  weights  and 


414          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.  [8J 

corrections,  the  definitive  declinations  are  computed  (as  they  appear  in  the  cata- 
logue at  the  end  of  this  paper),  a  few  excepted  which  depend  on  a  small  number  of 
authorities. 

9.  The  computation  of  a  few  systematic  corrections  to  catalogues  of  the  third 
class;  and  the  formation  of  all  remaiuing  declinations  for  the  final  catalogue. 

10.  A  few  deductions  relative  to  the  accuracy  of  the  declinations  formerly  adopted 
in  obtaining  latitudes  on  the  Northern  Boundary. 

SECTION   I. 

SELECTION  OP  STAGS. 

The  preliminary  catalogue  necessarily  embraces  all  the  stars  used  in  zenith  tele- 
scope work  of  the  United  States  Northern  Boundary  Commission,  1872-187/5. 

All  of  the  stars  of  the  American  Ephemeris  for  which  apparent  places  are  given  in 
that  publication  are  added  to  this  list,  Sirius  and  Procyon  excepted.  The  great 
majority  of  these  stars  are  required  for  the  purpose  of  constructing  the  normal  system. 
These  were  supplemented  by  a  considerable  number  of  the  Poulkova  Hauptsterne, 
preference  being  given  to  those  most  frequently  observed  at  Poulkova  and  elsewhere. 

At  the  suggestion  of  others  a  few  stars  were  added  which  might  servo  for  latitude 
determinations  with  zenith  telescope  on  or  near  the  parallel  of  39°  north  latitude. 

Effectively,  the  selection  may  be  regarded,  for  convenience,  as  embracing  at  least 
five  different  classes  of  stars : 

a.  The  fundamental  and  principal  circumpolar  stars  which  have  been  by  common 
consent  quite  universally  observed. 

6.  A  class  of  stars  less  frequently  observed,  but  with  the  observations  so  distrib- 
uted in  time,  that  reliable  determinations  of  declination  and  proper  motion  can  be  had 
without  recourse  to  Bradley's  observations;  and  which,  together  with  the  fundamental 
stars,  may  serve  to  construct  an  approximate  normal  system  for  the  epoch  1755. 

c.  A  class  of  stars  similar  to  the  last,  but  lacking  in  satisfactory  authorities  for 
the  epochs  included  between  1820  and  1840.    After  the  systematic  corrections  of  the 
older  authorities  are  ascertained,  these  will  serve  equally  with  the  preceding  in  deter- 
mining the  systematic  corrections  required  by  the  principal  authorities. 

d.  A  considerable  number  of  stars,  which  do  not  furnish  proper  material  for  ascer- 
taining systematic  corrections  to  the  principal  authorities,  but  which  will  be  found 
valuable  for  the  purposes  of  perfecting  the  system  of  corrections  adopted  for  a  few 
catalogues  of  small  weight,  and  for  extending  the  system  to  catalogues  deficient  in 
observations  of  the  first  three  classes  of  stars. 

e.  The  remaiuing  declinations  are  such  as  depend  on  few  authorities,  and  are  prac- 
tically of  no  service  in  ascertaining  systematic  corrections.    They  belong  to  the  class 
of  stars  selected  and  used  for  observation  with  the  zenith  telescope;  and  it  is  desirable 
to  calculate  their  declinations  with  whatever  precision  can  be  attained  by  the  use  of 
all  authorities  that  are  conveniently  accessible. 


[9] 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          415 


SECTION  II. 
APPROXIMATE  POSITIONS  FOB   1875.0. 

Our  plan  contemplates  the  assumption  at  a  given  epoch  of  approximate  values  of 
the  right  ascension  and  declination,  and  of  proper  motion  in  both  co-ordinates.  These 
will  serve  for  the  accurate  computation  of  the  precession  coefficients.  For  this  pur- 
pose it  is  simply  necessary  to  avoid  errors  which  are  largo  enough  to  introduce  appre- 
ciable errors  in  those  terms  of  precession  in  declination  that  depend  on  the  higher 
powers  of  the  time,  and  in  the  geometrical  part  of  the  annual  variation.  It  is,  however, 
desirable  in  order  to  facilitate  subsequent  computations  that  the  declination  and  its 
proper  motion  should  be  so  determined  that  the  corrections  they  may  require  will 
not  be  inconveniently  large;  and  that  the  difference  between  the  assumed  and  con- 
cluded proper  motions  will  not  be  so  large,  that  the  neglect  of  the  small  difference 
between  the  adopted  mean  epoch  of  observation  for  each  catalogue  and  the  particular 
mean  for  a  given  star  will  seriously  affect  the  final  result  for  declination  and  proper 
motion. 

The  epoch  of  reduction  selected  for  the  catalogue  is  the  fictitious  or  Besselian 
epoch  1875.0. 

Right  ascension. 

For  the  fundamental  stars  this  is  copied  from  Professor  Newcomb's  paper,  Appen- 
dix III.,  Washington  Observations  for  1870.  The  proper  motions  are  from  the  same 
source. 

Except  for  stars  south  of  declination  —  30°,  the  remaining  right  ascensions  are 
taken  from  the  American  Ephemeris  for  1875,  as  far  as  possible.  The  following  incon- 
siderable corrections  are,  however,  applied  in  most  cases.  They  are  intended  to  reduce 
these  right  ascensions  to  the  standard  of  Professor  Newcomb's  paper,  above  cited. 


Hour. 

Correction. 

Hour. 

Correction. 

Hour. 

Correction. 

8. 

s. 

8. 

0 

+  .03 

8 

—  .03 

1C 

+  .01 

1 

+  .02 

9 

—  .02 

17 

+  .02 

a 

+  .01 

10 

—  .02 

18 

+  .03 

3 

+  .01 

11 

—  .02 

19 

+  .03 

4 

00 

12 

—  .01 

20 

-t-  .03 

5 

—  .01 

13 

—  .01 

21 

+  .03 

C 

—  .01 

14 

-  .00 

22 

+  .03 

7 

—  .02 

15 

+  .01 

23 

+  .03 

8 

—  .02 

16 

+  .01 

24 

+  .03 

The  proper  motions,  in  A.  R.,  of  these  stars  were  taken  from  the  Star  Tables  of 
American  Ephemeris  (Wu.,  1869).  They  are  mostly  those  of  Dr.  B.  A.  Gould's  Stand- 
ard Places  of  Fundamental  Stars,  United  States  Coast  Survey,  second  edition  (Wn., 
18GC).  For  other  stars  the  A.  R.  and  /*  were  computed,  if  possible,  from  at  least  two 
good  modern  authorities  compared  with  either  Bradley,  Piazzi,  or  Groombridge,  and 


416          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.  [10] 

occasionally  with  all  three.  The  authorities  were  first  corrected  by  the  tables  of  Pro- 
fessor Newcomb's  paper  just  mentioned.  In  a  few  cases  where  older  authorities  were 
wanting  the  assumed  A.  R.  and  /x  were  computed  with  greater  care. 

Declinations. 

In  computing  assumed  declination  and  proper  motion  in  declination,  the  preference 
was  given:  first,  to  the  Northern  Boundary  catalogue  of  latitude  stars  for  the  epoch 
1874.0;  second,  to  the  declinations  for  1870.0  reduced  by  Brnhusfor  the  Gradmessung, 
and  contained  in  Qeneralbericht  dcr  Europaisclien  Gradmessung  fur  1871;*  third,  exclud- 
ing stars  south  of  —30°  declination,  to  the  declinations  for  1875.0  of  the  American 
Ephemeris ;  and  fourth,  in  the  failure  of  these  three  sources  of  supply,  declinations 
•were  computed  in  a  manner  entirely  analogous  to  that  adopted  with  right  ascensions, 
except  that  no  systematic  corrections  were  applied.  Nearly  all  the  declinations  of 
stars  south  of  —  30°  declination  were  formed  from  the  mean  of  Mr.  Stone's  recent 
catalogue  of  Maclear's  observations  at  the  Cape  for  I860,  and  the  First  Melbourne 
Catalogue  for  1870,  the  assumed  proper  motions  being  copied  from  the  latter.  '  In 
"  Details  of  Corrections  to  Assumed  Places "  the  preliminary  a  and  8  with  their 
assumed  variations  are  given  at  the  head  of  the  table  for  each  star. 


SECTION    III. 

COMPUTATION  OF  PRECESSION  TERMS. 

The  constants  of  Peters  and  Struve  have  been  adopted.    They  aref: — 

TO  =  46".0623  +  0".0002349  (t  —  1800) 
n  =  20".0607  -  0".00008C3  (t  —  1800), 

where  t  is  expressed  in  years.    These  are  now  in  very  general  use,  and  probably  are 
not  far  from  the  correct  values.  J 

At  any  rate,  since  our  object  is  not  so  much  to  ascertain  the  exact  amount  of 
proper  motion  as  to  know  the  total  change  produced  by  the  annual  movement,  great 
accuracy  is  required  only  in  terms  of  precession  involving  higher  powers  of  the  time. 
The  effect  of  proper  motion  has  been  considered  in  every  case,  and  for  this  purpose 
the  formula  given  by  Professor  Hill  in  Star  Tables  of  the  American  Ephemeris  (p.  xix) 
have  been  adopted.  The  coefficient  of  t3  has  received  a  slight  modification  due  to  the 
neglect  of  small  terms.  So  that,  if  the  first  and  second  differential  coefficients  in  both 

*  "  Die  Declinationen  der  bei  der  Gradmessung  zu  Bnitenbestimmungen  benutzten  Fixsterne,"  C.  Sruhns. 
The  declination  and  n'  of  a  Cephei  there  given  appear  to  lie  in  error.  Taking  the  geometrical  precession 
as  computed  on  p.  14,  the  seconds  of  (!  for  Bradley 's  observations  reduced  to  1870,  should  he  04".23  instead 
of  06".26  as  printed  in  the  last  column  of  p.  7.  The  corrected  proper  motion  will  be  -f-  ".024  instead  of 
+  ".006,  and  the  seconds  of  <i  for  1870,  7".  13  iustead  of  7".03. 

t  Numerus  Constant  Nutalionis,  pp.  CG,  71.    Dr.  C.  A.  P.  Peters. 

t  Dr.  C.  Bruhns  in  "  Die  DecUnationen  der  bei  der  Gradmessung,"  n.  s.  u.,  takes  the  same  course,  *  *  * 
"da  dieselbe  [precession  of  Struve]  zieischen  dem  Werthe  der  BesseVschen  und  der  Leverrier'schen  Prcecession 
licgt  und  nach  dm  neueren  Beobaclitungen  die  Variatio  scecularis  von  Strm-e  und  Leverrier,  die  fast  identisch  ist, 
entschieden  genauer  als  die  BesseVsche  Variatio  saxularis  sichfindet,"  pp.  2  and  3 


fllj  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          417 


co-ordinates  are  known,  tbe  computation  of  -575  will  be  sufficiently  rigorous,  simple, 
and  expeditious.    In  computing 


—  is  usually  without  sensible  influence  on  the  result.    Let 

(it 

a    and  3     =  respectively  the  right  ascension  and  declination  of  a  star, 
,'j.    and  /*'    =  the  corresponding  proper  motions, 
n    and  m    =  coefficients  of  precession, 

dn       ,  dm 

-T  and  -      =  their  respective  annual  variations. 


We  shall  have:  — 

—  =m 
dt 


sin  a  tan  S 


—  =  n  cos  a  +  //.' 
dt 

_^  =  n  [i  cos  a  tan  S  -f  n  //  sia  a  sec2  8  +  2  /i  /»'  tan  * 
at 

~l-  =  —  n  11  sin  a  —  J  //  sin  25 

HV 

<Z2a          wt  <?n  .  dm  .  dn  1  /rfa        "\   .      /da  .     \ 

-r*  =  ---  r-  +  -73-  +  -;  --  (  TT  —  I1  I  +n(  -T-  +  /4  )  COS  a  tan 

d«2  71  dt       dt       dtn  \dt        /         \dt        J 

^  +  [>T\  sin  a  sec2  S  +  2  /*  //  tan  3. 


If  a,  //,  m,  and  -^i  are  expressed  in  time,  and  the  factor  -=  supplied,  when  necessary, 

tit  ft 

we  have  the  following  tables  of  logarithmic  values  for  the  coefficients,  the  arguments 
being  the  year,  and  quantities  depending  on  the  place  of  the  star,  except  for  the  first 
table,  which  simply  gives  the  values  of  m  and  n  for  various  epochs:  — 


Year. 

M 

7!. 

logrc 

10*1T 

8. 

/. 

1750 

3.  06987 

20.  0650 

1.  30243&5 

0.  126348 

1775 

3.  07035 

20.  0629 

1.  30239^8 

0.  126302 

1800 

3.  07082 

20.  0607 

1.  3023461 

0.  126255 

1825 

3.  07129 

20.0585 

1.  3022994 

0.  126208 

1850 

3.07177 

20.  0564 

1.  3022527 

0.126162 

1875 

3.07225 

20.  0542 

1.3022059 

0.  126115 

1900 

3.  07272 

20.0521 

1.  3021592 

0.  126068 

N  B- 


-27 


418          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.  [12] 

(Pa 


Log.  coefficients  of  — 

Year. 

Constant. 

£-/• 

dt      p 

(  |^  +  /i  J  cos  a  tan  <S 

(  ~J7-|-/<    )smasec2<! 

/i  /*'  tan  <5 

(  —  101 

(-10) 

(-10) 

(-10) 

1750 

+  .  0000  3220 

4.  63357  » 

5.  98801 

4.81192 

4.1866 

1775 

3220 

4.  63362  n 

5.  98797 

4.81168 

< 

1800 

3220 

4.  63366  re 

5.  98792 

4.81183 

< 

1825 

3221 

4.  63371  re 

5.  98787 

4.  81178 

t 

1850 

3221 

4.63376m 

5.  98783 

4.  81174 

4 

1875 

3221 

4.  63380  re 

5.  98778 

4.  81  169 

< 

1900 

+  .  OOQP  3222 

4.  63385  re 

5.  98773 

4.  81164 

t 

Log.  coefficients  of  — 

Year. 

if  sin  2d 

(5-0 

(S+>)- 

1750 

(-10) 
6.73673m 

(-10) 
4.  63357  re 

(-10) 
7.164105m 

1775 

4.  63362  re 

7.  104059  n 

1800 

4.  63366  ra 

7.164012m 

1825 

4.  63371  m 

7.  103965m 

1850 

4.  63376  re 

7.  16391  8  re 

1875 

4.  63380  n 

7.  163872  re 

1900 

4.63385n 

7.  163825  n 

(P6 
dt3 


Log.  coefficients  of  — 

Year. 

/da      ft\ 

(S+3)— 

/^a          \   /^da\ 

1750 

(-10) 
2.09871 

(-10) 
7.  16411  re 

(-10) 
3.  02577  n 

1775 

7.  16406  re 

3.  02573  re 

1800 

7.  16401  re 

3.  02568  re 

1825 

7.  16396  re 

3.  025G3  re 

1850 

7.  16392  re 

3.  02558  m      • 

1875 

7.  16387  n 

3.  02554  n 

1900 

7.  16383  n 

3.  02549  re 

[13]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  419 

With  these  tables,  and  with  the  assumed  values  of  a,  d,  //.,  and  //.',  ~,  —  ",  —  ,  -_ 

and  —  were  computed  for  the  epoch  1875  for  every  star.    The  values  of  all  these  will 
dt3 

be  found  in  the  definitive  catalogue  (end   of  this  Appendix),  except  that  of  —  ,  for 

which  the  catalogue  gives  the  corrected  value.    The  assumed  value  of  —  and  -?-  will 

be  found  with  assumed  values  of  a  and  <J  at  the  head  of  the  table  for  each  star  in 
"  Details  of  Corrections  to  Assumed  Places." 

Having  now  assumed  declinations  and  variations  in  precession  for  1875.0,  the 
position  for  any  other  date,  T  will  be:  — 


By  this  formula  the  declinations  of  all  the  Nautical  Almanac  stars,  with  otbers 
most  frequently  observed,  were  computed  for  the  dates  1755,  1800,  1810,  1820,  and  for 
each  succeeding  year  until  1875.  Stars  less  frequently  observed  were  computed  only 
to  those  dates  actually  required.  The  computation  in  every  part  was  carefully  scrutin- 
ized, and  either  checked  by  differences  or  duplicated. 

For  stars  within  5°  of  the  pole,  and  for  one  or  two  others  at  particular  dates,  the 
above  proceeding  will  not  answer.  These  were  rigorously  reduced  by  the  trigonomet- 
rical formula  to  the  required  dates  before  and  to  every  five  years  after  1820  from  places 
and  proper  motions  assumed  for  the  epoch  1855.  The  following  formula,  taken  from 
Chauvenet's  Spherical  and  Practical  Astronomy  (vol.  i,  p.  615),  were  used:— 

p  =  sin  0  (tan  8  +  tan  \  0  cos  A] 

.  ,  p  sin  A 

tan  (A1  —  A)  =  —£- 

1  —  p  cos  A 


in  which 

A  —  a  +  z  -f-  #,  and  A'  =  a'  —  z'  +  #', 

a  and  a'  being  respectively  the  assumed  and  required  right  ascensions,  #  the  planetary 
precession,  and  z,  z',  and  0  are  found  from  the  formulae  :— 

tan  £  (z1  +  s)  =  tan  J  (<//'  —  >//)  cos  £  (EI'  +  EI) 

£  (s/  —  *)         ==  tan  £  (</-'  —  '/')  8lu  i  l£i'  +  £i) 
sin  J  0  =  sin  £  (y'  —  '/')  sin  J  (E!'  +  e^, 

where  the  symbols  used  have  the  same  signification  as  in  the  place  from  which  the 
formula?  are  cited.  Reckoning  from  1800,  we  have  $  =  +  7".584.  For  the  other  quan- 
tities I  have  computed  the  following  table: — 


420 


UNITED  STATES  NOBTHEEN   BOUNDARY  COMMISSION. 


[14] 


Table  giving  values  of&',  «,«•,*  0,  log.  tan  £  0,  and  log.  sin  0,  in  the  formulae  for  reducing 

star  places,  from  1855,  to  other  dates. 


Date. 

& 

z 

21 

iO 

log.  tan  i  9 

log  sin  0 

a 

i   it 

/     // 

/      It 

(-10) 

(  —  10) 

1755 

—  7.293 

—  38  31.  402 

—  38  29.  890 

—  16  42.  994 

7.  6868766  n 

7.  9878963  n 

1790 

—  1.536 

—  25  05.  201 

—  24  58.  399 

—  10  51.  904 

7.  4997603  n 

7.  8007864  n 

1800 

000 

—  21  14.  881 

—  21  06.567 

—  9  11.601 

7.  4272008  n 

7.  7282277  » 

1805 

+  0.750 

—  19  19.726 

—  19  10.  656 

—  8  21.  450 

7.  3858037  n 

7.  6868312  n 

1810 

+  1.488 

—  17  24.574 

—  17  14.748 

—  7  31.301 

7.  3400421  n 

7.  6410700  n 

1815 

+  2.  213 

—  15  29.  423 

—  15  18.841 

—  6  41.  152 

7.  2888849  n 

7.  5899133  n 

1820 

-f  2.927 

—  13  34.274 

—  13  22.  936 

—  5  51.  005 

7.  2308885  n 

7.  5319172  n 

1825 

+  3.629 

—  11  39.  131 

—  11  27.037 

—  5  00.  858 

7.  1639373  n 

7.  4649665  n 

1830 

+  4.318 

—  9  43.  989 

—  9  31.  139 

—  4  10.713 

7.  0847517  n 

7.  3357811  « 

1835 

+  4.995 

—  7  48.849 

—  7  35.243 

—  3  20.568 

6.  9878370  n 

7-.  2888666  n 

1840 

+  5.661 

—  5  53.  712 

—  5  39.  350 

—  2  30.  424 

6.  8628935  n 

7.  1639233  » 

1845 

+  6.314 

—  3  58.  577 

—  3  43.459 

—  1  40.232 

6.  6867983  n 

6.  9878282  n 

1850 

+  6.955 

—  2  03.  448 

—  1  47.568 

—  0  50.  140 

6.  3857631  n 

6.  6867930  n 

1855 

1860 

+  8.201 

+  1  46.812 

+  2  04.  198 

+  0  50.  139 

6.  3857545 

6.  6867844 

1665 

+  8.805 

+  3  41.  937 

+  4  00.  079 

+  1  40.278 

6.  6867794 

6.  9878093 

1870 

+  9.398 

+  5  37.  061 

-)-  5  55.957 

+  2  30.415 

6.  8628659 

7.  1638957 

1875 

+  9.979 

-f-  7  32.  179 

+  7  51.  833 

+  3  20.551 

6.  9877997 

7.2888293 

SECTION  IV. 

SELECTION  OF  AUTHORITIES. 

Nearly  all  authorities  for  declination  which  were  conveniently  accessible  have 
been  selected  for  use.  The  scattered  observations  in  astronomical  journals,  and  zone 
observations,  with  a  few  others  of  small  weight,  have  generally  been  neglected.  For 
convenience  I  have  divided  them  into  three  classes,  for  reasons  which  will  subse- 
quently appear. 

CLASS  I. 

Embraces  catalogues  and  series  of  observations  which  have  been  adopted  in  con- 
struction of  the  normal  system.  The  designation  of  each  catalogue  is  first  given, 
the  principle  of  nomenclature  being  that  the  letters  usually  indicate  the  first  and  final 
letters  in  the  name  of  the  observatory  according  to  the  English  spelling,  and  the  fig- 
ures the  mean  year  of  observation,  roughly  estimated.  In  designating  the  various 
annual  catalogues  (as  well  as  compilations)  in  such  series  as  those  of  Greenwich  and 
Washington,  this  system  is  found  to  be  very  convenient. 

Kg  21.  Bessel's  observations  in  1820  and  1821  with  the  Eeichenbach  Circle,  pub- 
lished in  Kon.  Beol).  Bd.  vii.  Dollen's  discussion  has  been  adopted,  however.  This  is 
found  in  "Recueil  de  M&moires  des  Astronomes  de  VObservatoire  Centra  I  de  Russie?  vol. 
ii,  p.  203  to  232.  The  seconds  of  declination  are  adopted  from  column  headed  "B2"  in 
tables  iii  and  iv.  These  differ  from  Bessel's  own  reduction  (Kon.  Beob.  Bd.  vii)  by  the 
quantity 

+  ".30  +  0".56  sin  Z  +  ".023  tan  Z 

which  must  be  applied  as  a  correction  to  Bessel's  declinations.  The  declinations  so 
reduced  adopt  for  the  horizontal  flexure  +  0".5G,  which  is  the  mean  between  that  found 
by  Bessel  in  1820-'21,  from  reflection  observations,  and  afterward  by  horizontal  colli- 


[15]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          421 

mators.    The  reduction  of  the  observations  in  this  manner  is  found  to  correspond 
closely  with  Bessel's  observations  of  the  sun.* 

Gh  22.  Olufsen's  reduction  of  Pond's  observations  at  Greenwich  for  the  year  1822, 
printed  in  Ast.  Nach.  422. 

Dt  24.  Struve's  declinations  in  "  Catalugus  Primarius,  p.  xxxxviii,  Introduction 
"  Stcllarum  Fixarum  imprimis  Diiplicium  et  Multiplicium  Positiones  Media?  pro  Epocha 
1830.0." 

Ao  29.  The  ibo  Catalogue  of  Argelander,  "  DLX  Stellarum  Fixarum  Positiones 
Media,  ineunte  Anno  1830." 

S.  H.  31.  Johnston's  St.  Helena  catalogue.  "A  Catalogue  of  606  Principal  Fixed 
Stars  in  the  Southern  Hemisphere,  deduced  from  observations  made  at  the  observ- 
atory, St.  Helena,  from  November,  1829,  to  April,  1833."  The  epoch  of  reduction 
is  1830. 

C.  G.  H.33.  Henderson's  declinations  derived  from  observations  made  at  the  Cape 
of  Good  Hope.  The  series  extends  from  May  16, 1832,  to  May  24, 1833,  and  is  reduced 
to  the  mean  epoch  1833.  It  is  found  in  Memoirs  of  the  Royal  Astronomical  Society, 
vol.  x,  p.  80. 

Ce  34.  Airy's  observations  at  Cambridge,  England,  taken  in  the  years  1833,  '34, 
and  '35,  and  printed  in  the  annual  volumes  of  the  observatory  for  (hose  years. 

Eh  37.  Henderson's  observations  made  at 'the  Royal  Observatory  in  Edinburgh, 
in  the  years  1834-'39,  and  printed  in  the  annual  volumes  for  those  years. 

Kg  38.  Bessel's  declinations  observed  with  the  Reichenbach  circle  in  1836-'40. 
These  are  reduced  by  Busch,  and  the  results  are  found  in  Ast.  Nach.,  422. 

Gh  39.  Greenwich  observations,  which  form  the  first  part  of  the  Greenwich  Twelve- 
year  Catalogue.  They  arc  reduced  to  the  epoch  1840,  and  embrace  the  results  from 
two  mural  circles,  for  the  period  1830-1841. 

Ce  40.  These  are  the  first  observations  made  under  the  directorship  of  Rev.  J.  E. 
Challis.  They  extend  from  the  year  183G  to  1844,  both  inclusive,  and  are  taken  from 
Ihe  annual  catalogues  of  the  Cambridge  observatory. 

Eh  43.  Henderson's  Edinburgh  results  found  in  annual  catalogues  1841-'44.  They 
are  reduced  by  Professor  Smyth. 

Kg  43.  There  are  three  reductions  of  this  series.  I  have  used  that  found  in  Ast. 
Nach.,  1076,  made  by  Luther.  The  observations  were  made  in  years  1842-'41,  by  Bes- 
sel,  at  the  Kouigsberg  observatory,  with  Repsold  circle. 

Gh  45.  Second  part  of  the  Greenwich  Twelve-year  Catalogue,  embracing  Green- 
wich observations  1842-1847,  reduced  to  the  epoch  1845. 

Pa  45.  The  catalogue  of  declinations  given  for  the  epoch  1845.0  in  the  fourth  vol- 
ume of  "  Observations  de  Poulkova"  (p.  50).  The  observations  were  made  with  the  ver- 
tical circle  by  Dr.  Peters,  in  1842-1849,  and  the  reductions  are  partly  made  by  him  and 
partly  by  Dr.  Gylden. 

Re  45.  First  "Radcliffe  Catalogue  of  6317  Stars  chiefly  circumpolar,  reduced  to 
the  Epoch  1845  0,"  Johnson. 

Wn  47.  The  annual  catalogues  of  the  Washington  observatory  for  the  years  1845- 
1848  inclusive.  The  observations  are  made  with  the  mural  circle,  by  various  observ- 
ers. (The  results  of  the  four  succeeding  years  occasionally  exhibit  enormous  discrep- 

•  Vide  Pollen's  Memoir,  p.  221. 


422          UNITED  STATES  NOETHEEN  BOUNDAEY  COMMISSION.  [16] 

ancles  both  among  themselves  and  when  compared  with  the  approximate  places  above 
mentioned.    No  use  is  made  of  these  four  catalogues,  1849-1852.) 

Ce  48.  Cambridge  (Eng.)  animal  catalogues,  1845-1851. 

Gh  51.  Greenwich  Six-year  Catalogue,  epoch  1850. 

Ps  53.  Laugier's  declinations  with  the  Garnbey  circle  at  Paris  observatory,  princi- 
pally made  in  the  years  1852  and  1853,  and  reduced  to  the  epoch  1852.  They  are 
taken  from  pp.  72  to  74  of  "  Memoire  sur  la  Determination  des  Distances  Polaires  des 
Etoiles  FondamentaleSj  par  E.  Laugier,"  tome  xxvii,  2e  partie  des  Memoircs  dc  V Academic 
des  Sciences. 

So  55.  Moesta's  declinations  with  the  Pistor  and  Martin's  circle  at  Santiago  in  the 
years  1853-1855,  reduced  to  the  epoch  1855,  and  printed  in  "  Observationes  Astronomi- 
cas  heckas  en  el  Obserratorio  National  de  Santiago,  en  los  aiios  de  1853, 1854,  y  1855,  por 
el  Dr.  Carlos  Guillerruo  Mosta,  director  del  observatorio."  Tomo  I.  Santiago  de  Chile 
1859. 

Wn  5P>.  This  series  embraces  observations  with  the  Washington  mural  circle  in 
the  years  1853-1858.  They  are  reduced  and  the  results  printed  in  Appendix  II.,  Wash- 
ington observations  for  1870.  Prof.  A.  Hall  has  formed  the  declinations  of  the  funda- 
mental stars  into  a  single  catalogue,  printed  in  Ast.  Nacli.  1947.  I  have  taken  the 
declinations  from  the  original  source. 

Gh  57.  The  Greenwich  Seven-year  Catalogue  of  2022  Stars  reduced  to  the  epoch 
1860.0.  The  observations  embrace  the  years  1854-1860  inclusive. 

C.  G.  H.  58.  Observations  made  with  the  Cape  circle  in  the  years  1856-'61  by  Sir 
Thomas  McClear,  reduced  to  the  epoch  1860  by  E.  J.  Stone,  astronomer  royal  at  the 
Cape  of  Good  Hope,  and  printed  in  "  The  Cape  Catalogue  of  1159  Stars,"  etc.,  Cape 
Town,  1873. 

Wn  64.  Eesults  of  observations  with  Washington  mural  circle  for  the  years  1861- 
1865,  printed  in  the  annual  catalogues  of  the  respective  years. 

Gh  64.  The  new  Seven-year  Catalogue  of  Greenwich,  embracing  the  results  of 
observations  with  the  Greenwich  transit  circle,  for  the  years  1861-1867,  both  inclusive. 

Lu  67.  This  series  is  taken  from  "  Mittlere  Declinationen  von  57  Fundamental 'sternen, 
abgeleitct  aus  Leidener  Merldiarikreisbeobachtungen  in  den  JaUren  1864-1868,"  W.  Val- 
entine (Ast.  Nach.  K  902  Bd.  80,  s.  93);  and  from  "Annalen  der  Sternwarte  in  Leiden, 
herausgegcben  von  Dr.  F.  Kaiser." 

Me  68.  "The  First  Melbourne  General  Catalogue  of  1227  Stars,  for  the  Epoch 
1870.  Deduced  from  Observations  extending  from  1863  to  1870,  made  at  the  Melbourne 
Observatory,"  etc.  11.  L.  J.  Ellery,  Melbourne,  1874. 

Wn  68.  Eesults  of  observations  made  with  the  Washington  transit  circle  in  the 
years  186G-1869,  taken  from  the  annual  volumes. 

Ee  OS.  Eesults  of  observations  made  with  the  Cariingtou  circle  at  the  Badcliffo 
observatory  in  the  years  1862-1873.  These  are  taken  from  the  annual  catalogues  of 
the  Eadcliffe  observatory.  They  are  finally  divided  into  two  series — Ee  66,  including 
years  1862-1869;  Ee  72,  including  years  1870-1873. 

Gh  70.  Eesults  of  observations  made  with  the  Greenwich  transit  circle  and  printed 
in  the  annual  catalogues  of  the  Greenwich  observatory,  1868-1872. 

Wn  72.  Eesults  of  observations  with  the  Washington  transit  circle  1870-1874, 
printed  in  annual  volumes.  The  results  of  1874  in  manuscript  were  generously  placed 
at  my  disposal  by  Prof.  J.  E.  Eastman. 


[17]  EBFOET  OF  THE  CHIEF  ASTEONOMEE,  APPENDIX  H.          423 

CLASS  II. 

This  embraces  catalogues  supposed  to  be  unsuitable  for  use  in  founding  the  normal 
system ;  but  excludes  a  few  catalogues  of  small  extent,  or  weight,  which  are  used  only 
with  stars  of  class  e.  Many  of  these  are  the  results  of  observations,  which  in  turn 
depend  on  the  places  of  a  standard  list  of  stars;  others  are  independent,  but  of  small 
weight;  or  their  use  for  other  reasons  may  be  regarded  as  of  doubtful  propriety. 

Gli  1752  or  Gh  1755.  "  Fundamenta  Astronomies  pro  Anno  MDCGLV.  deducta  ex 
Observationibus  Viri  Incomparabilis  James  Bradley  in  Specula  Astronomica  Grenovicensi 
per  Annos  1750-1762  institutis,  Auclore  Fredcrico  Wilhelmo  Bessel."  Regiowonti  1818. 
This  is  in  effect  the  result  of  two  series  of  observations — the  one  of  northern  stars 
(stars  north  of  Greenwich  zenith),  mean  epoch  about  1752;  the  other  of  southern 
stars,  mean  epoch  1755  or  1750. 

Po  1800.  "  Precipuarum  Stcllarum  Inerrantium  Positiones  Media  inuente  sceculo 
XIX.  Ex  observationibus  kabitis  in  Specula  Panormilana  ab  anno  1792  ad  annum 
1813,"  Panormi  1814,  by  Joseph  Piazzi. 

Bh  10.  "A  Catalogue  of  Circumpolar  Stars,  deduced  from  the  Observations  of  Ste- 
phen Groombridge,  Esq.",  &c.,  at  Blackheath  observatory.  Eeduced  to  January  1, 
1810,  and  edited  by  Sir  G.  B.  Airy.  Lond.  1838. 

Va  29.  Professor  Littrow's  declinations  of  fundamental  stars,  from  observations 
made  at  the  Vienna  observatory  in  the  years  1827-'8-'9.  They  are  reduced  to  1830, 
and  printed  in  Mem.  Boyal  Ast.  Soc.  IV.,  p.  328. 

Dt  30.  Struve's  Positiones  Medice,  above  cited,  Catalogus  Generalis,  These  places 
are  quite  numerous  and  appear  to  be  when  correctiones  ultimw  are  applied,  systemati- 
cally the  same  as  the  results  of  Catalogus  Primarius.  The  observations  from  which  the 
catalogue  is  constructed  extend  over  the  period  1822-1843,  however,  and  there  were 
consequently  doubts  whether  Dt  24  and  Dt  30  should  be  classed  together. 

Gh  30.  Pond's  catalogue  of  1112  stars  reduced  to  1830.  These  are  the  results  of 
observations  made  with  two  mural  circles  from  January  1,  1825,  to  January  1,  1833. 

C.  G.  H.  31.  Eesults  obtained  by  Fallows,  in  1830  and  1831,  at  the  Cape  of  Good 
Hope;  reduced  to  1830,  and  printed  in  Mem.  E.  A.  S.  vol.  XIX.  The  catalogue  con- 
tains but  few  declinations,  and  has  only  been  used  with  a  few  stars  south  of  —30°. 

Mh  34.  The  results  of  Lamont's  observations  at  Munich  in  the  years  1829-1840. 
Most  of  the  observations  were  made  in  1833  and  1834,  and  are  found  in  "  Observations 
Astromicos  in  Specula  Regia  Monacliiensi^  etc.,  for  those  jears.  I  have  for  convenience 
taken  all  from  '•'•Annalen  der  Koniglichen  Stermcarte  bei  Munchm,"  Bd.  XX.,  Miiucben, 
1874;  and  from  the  detailed  positions,  commencing  p.  264. 

Ah  41  and  Ah  52.  Ejbinson'n  Armagh  catalogue  of  5345  stars.  Owing  to  the 
great  period  o"  time  embraced  in  the  observations  of  this  catalogue,  I  have  divided 
them  into  two  series— the  first,  for  the  years  1835-1846;  the  second,  1847-1854.  This 
I  have  done  by  a  method  which  will  be  explained  (p.  39). 

So  51.  The  observations  of  Captain  Gillis  made  at  the  observatory  of  Santiago, 
in  Chili,  in  the  years  1850-1852.  The  catalogue  reduced  to  1850  is  printed  in  Appen- 
dix I.,  Washington  Astronomical  Observations  for  1868. 

Bs  66,  Bs  60,  Bs  05.  These  are  to  be  found  in  "  Annales  de  VObservatoire  Eoyal  de 
Bruxelles ",  for  years  1855-1867.  The  groups  are:  1855-1856;  1857-1862;  1803-1807. 

Ps  56  and  Ps  CO.  These  are  found  in  " Annales  de  VObservatoire  Imperial  de  Paris." 


424          UNITED  STATES  NOETHEEN   BOUNDAEY  COMMISSION.  [18] 

The  first  group  covers  the  years  1854-1857,  the  second  1858-1862;  and  both  are  the 
results  of  observations  of  the  Gambey  mural  circle. 

Ps  64  and  Ps  66.  These  are  in  continuation  of  the  series  just  mentioned,  bat  the 
observations  are  principally  made  with  the  great  meridian  circle  of  Eichens  and  Secre- 
tan.  The  groups  are  1863-1864,  and  1865-1867. 

Ce  56.  This  series  embraces  the  annual  catalogues  in  the  volumes  of  the  Cam- 
bridge (Eng.)  observatory  for  the  years  1852-1860. 

Ee  58.  "  Second  Kadclifi'e  Catalogue  containing  2386  stars;  deduced  from  observa- 
tions, extending  from  1854  to  1861, at  the  Badcliffe  observatory,  Oxford;  and  reduced 
to  the  epoch  1860." 

Me  62.  "Astronomical  Observations  made  at  the  Williamstown  Observatory  in  the 
years  1861,  1862  and  1863,  under  the  direction  of  Eobert  L.  J.  Ellery,"  etc.  Eeduced 
to  1860.  Melbourne,  1869. 

Bn  66.  Argelander's  observations  with  the  transit  circle  at  Bonn  observatory. 
These  are  found  partly  in  Ast.  Nach.  No.  1719,  and  partly  in  Bonn  Beob.  Bd.  VI. 

Lc  67.  "  Rexultata  aus  Beobachtungen  avf  der  Leipziger  Stcritwarte,"  Dr.  Eugle- 
mann,  1870;  also  " Die  Declinationen  der  bei  Gradmesstmg"  etc.,  Dr.  C.  Bruhns. 

CLASS  III. 

When  an  authority  is  of  small  weight,  and  especially  when  it  has  few  declinations 
in  common  with  the  standard  stars  of  Section  VIII,  there  is  danger  that  the  error  in 
adopted  systematic  correction  for  computing  the  definitive  declinations  may  work  a 
disadvantage,  which  will  more  than  counterbalance  any  benefit  to  be  derived  from 
supposed  additional  weight.  This  objection  will  be,  in  a  measure,  removed  by  the 
computation  of  a  large  number  of  definitive  places,  giving  more  and  better  standards 
for  comparison. 

In  making  up  this  list  a  few  series  of  observations  have  been  omitted,  either 
because  they  were  not  at  my  disposal,  or  because  it  was  believed  that  the  labor  of 
collating  them  and  ascertaining  the  proper  reductions  and  correclions  would  not  be 
repaid  by  the  weight  of  new  material  thus  acquired.  Zone  observations  for  the  most 
part  are  neglected  on  account  of  their  small  weight  in  a  discussion  of  this  kind.  A 
very  few  of  Lalande's  and  D'Agelet's  observations  were,  however,  used  in  extreme 
cases. 

Ms  35.  "General  Catalogue  of  the  Principal  Fixed  Stars,  from  Observations 
made  at  Madras,  by  T.  G.  Taylor."  Madras,  1845.  The  declinations  are  reduced  to 
the  epoch  1845. 

Ms  50.  Astronomical  observations  made  at  Madras  for  the  years  1848-1852.  Mad- 
ras, 1856. 

Wn  48.  Declinations  from  the  prime  vertical  transit  at  Washington,  principally 
in  the  years  1847  and  1848. 

Eh  08,  Eh  63,  and  Eh  67.  Edinburgh  astronomical  observations.  The  groups  are 
respectively  1854-1860;  1861-1864;  and  1865-1869.  The  declinations  are  taken  from 
the  annual  catalogues. 

Pa  62.  "  Observations  faites  a  Vlustrumtnt  des  Passages  e"labli  dans  le  premier  Verti- 
cal," volume  iii,  "  Observations  de  Poulkova,"  pp.  224  to  237.  The  declinations  are 
determined  by  Mr.  F.  A.  Oom. 


1 19]  KEPOET  OF  THE  CHIEF  ASTEONOMEE,  APPENDIX  H.  425 

Wu  70.  Declinations  by  Prof.  M.  Yarnall  with  the  mural  circle  of  tbe  Washington 
observatory,  1SGG-1873,  taken  from  the  detailed  results  in  annual  volumes  of  Wash- 
ington Astronomical  Observations. 

Pa  71.  In  the  ninth  volume  of  "  Viertcljahrsschrift  der  Astroncmisclien  Gesellschaft 
(pp.  83  to  88),  is  given  a  catalogue  of  the  u  Zusatzsterne"  from  observations  of  the 
Poulkova  observatory.  The  declinations  are  undoubtedly  of  a  high  order  of  accuracy; 
but  feeling  some  uncertainty  about  the  proper  manner  of  deducing  systematic  correc- 
tion from  them,  I  have  placed  them  in  Class  III.  ;  and  in  consequence  use  but  one  of 
the  declinations  for  definitive  purposes. 

SECTION  V. 

EXPLANATION   OF  PBELIMINABY  COBEECTIONS  AND   COMPILATION  OP  EESULTS. 

Before  proceeding  to  actual  discussion  of  normal  declinations,  it  will  be  necessary 
to  examine  each  catalogue  for  the  purpose  of  applying  such  corrections  as  shall  appear 
advisable  from  inspection.  These  corrections  may  be  regarded  as  of  three  classes  : 

First.  Those  required  on  account  of  the  reduction  of  the  observations  from  appar- 
ent place  to  the  true  epoch  of  the  catalogue.  These  are  principally  for  nutation  and 
proper  motion  actually  employed.  In  a  few  cases  small  corrections  have  been  applied 
to  reduce  from  epoch  "Jan.  1"  (Greenwich),  or  ©  =281°  to  the  fictitious  epoch  ©  = 
280°;  and  rarely,  a  correction  for  precession  which  is  always  practically  insignificant. 

Modern  researches  appear  to  show  that  no  considerable  correction  to  Peters's 
nutation  is  needed;  and  that  value  is  now  universally  used.  This  value  for  1800  is 
(Numerus  Constans  Nutationis  p.  37) : 

9".223  cos  &  sin  a  —  6".865  sin  &  cos  a. 

Among    other  rvalues  of  autation  that  have  been  used  in  reducing  observations  are 

these : — 

Value  employed  by  Bessel  in  Fund.  Ast 9".C48 

Bradley's  (original  value) 9".00 

Maskelyue's ' 9".55 

Groombridge's       9".G3 

Lindenau's • 8".977 

Baily's  (A.  S.  0.  and  B.  A.  C.)   .     .     . 9".25. 

The  individual  corrections  applied  to  each  catalogue  are  for  the  principal  terms, 
and  are  of  the  form 

17  sin  a  +  r/  cos  a, 

which  appears  to  require  no  explanation. 

In  most  cases  requiring  it  the  correction  for  proper  motion  has  been  applied.  It' 
t  denotes  the  epoch  of  reduction  of  the  catalogue  and  t'  the  mean  epoch  of  the  obser- 
vations of  a  particular  star  in  the  same,  //,  the  assumed  proper  motion  (Section  III.), 
and  n"  the  proper  motion  which  was  applied  in  the  reductions  of  the  catalogue,  we 
shall  have  corrections  for  proper  motion,  where  (t  —  I')  is  expressed  in  years : — 

(P.'  -  M")  (t  -  I'). 
Where  the  correction  is  practically  insignificant,  where  the  epoch  of  observation 


426          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.  [20] 

is  not  conveniently  ascertained,  where  redactions  are  inaccurate,  or  not  carried  beyond 
first  decimal  place  of  seconds,  and,  especially,  in  a  few  of  the  cases  where  proper 
motions  have  been  determined  by  comparison  with  Bradley,  this  correction  is  com- 
monly neglected. 

The  correction,  for  epoch,  i.  e.,  from  sun's  longitude  281°  or  from  "Jan.  1"  to  O  = 
280°,  is  applied  to  most  of  the  English  catalogues  whose  epoch  is  previous  to  1857,  and 
to  Wn  47. 

The  correction  for  precession  is  generally  insignificant,  and  is  often  included  in 
the  form,  An.  Var.  assumed  —  An.  Var.  of  Catalogue.  In  case  of  catalogues  which 
had  been  reduced  by  help  of  the  Astronomical  Society's  Catalogue  (Baily  1'830)  it  was 
convenient  to  include  a  correction  for  precession  with  that  for  epoch  and  nutation. 

Second.  In  many  catalogues,  corrections  which  have  been  derived  by  special  exami- 
nation of  the  instrument,  or  discussions  of  the  observations,  are  indicated  in  the  intro- 
ductions, but  not  applied  to  the  results.  Similar  corrections  sometimes  occur  through 
the  neglect  of  certain  precautions,  and  which,  discovered  too  late  for  correction  of  the 
printed  results,  are  in  the  nature  of  errata,  to  be  applied  by  the  reader.  Correctiones 
Ultimcc,  in  Struve's  Pos.  Ned.,  are  of  the  former  class ;  certain  corrections  in  the  intro- 
ductions to  the  two  Radcliffe  catalogues  are  of  the  latter  class.  Finally,  under  this  head 
come  errata  wherever  found. 

Third.  In  a  limited  number  of  cases  it  has  been  thought  advisable  to  examine  cer- 
tain series  of  annual  catalogues  in  order  to  reduce  the  discordances  in  the  results  of 
separate  years,  and,  if  possible,  to  ascertain  corrections  which  seem  to  be  required  by 
preliminary  inspection.  This  is  analogous  to  the  work  already  done  by  the  authors  in 
many  cases,  where  catalogues  have  been  formed  from  those  of  several  separate  years. 

Under  the  designation  of  each  catalogue  will  be  enumerated  all  the  corrections 
above  specified  which  have  actually  been  applied  in  this  discussion.  Some  of  the 
peculiarities  in  methods  of  observation  or  reduction  which  appear  to  invite  special 
attention  will  be  noticed  in  the  same  connection.  The  reasons  for  grouping,  and  the 
methods  of  combining  the  results  of  partial  catalogues,  will  be  explained. 

The  corrected  catalogue  declinations  are  then  compared  with  the  assumed  declina- 
tions of  this  paper  (Sections  II.  and  III.),  and  the  residuals,  in  the  sense  Observed- 
Assumed  Declinations  are  exhibited  in  column  "  C,"  in  "Details  of  Corrections  to 
Assumed  Declinations".  To  facilitate  comparisons  of  separate  years  in  the  case  of 
compilation,  the  subtraction,  Observed — Assumed  Declination  is  made  at  the  out- 
set, by  which  means  the  various  catalogues  are  effectively  referred  to  a  common  mean 
epoch,  with  the  assumed  annual  variations  (Section  II.).  These  residuals  are  then  com- 
bined with  or  without  correction,  as  the  case  may  require. 

Gh  1752-1755.  The  coefficient  of  nutation  adopted  by  Bessel  in  the  reductions 
is  9".G48.  Taking  the  mean  epoch  of  observation  for  northern  stars  to  be  1752,  and 
for  southern  1755,  the  corrections  to  the  declinations  will  be : — 

Northern  stars  —  ".34   sin  (a  —  53°.9) 
Southern  stars  —  ".425  sin  (a  —   2°.7) 

Before  discussing  the  systematic  correction,  the  corrections  applied  by  Bessel  to 
Bradley's  declinations  between  the  parallels  +  14°  and  —  14°  are  subtracted  from  the 
catalogue  places.  No  attempt  was  made  to  ascertain  proper  motion  corrections  on 


[21]  EEPOET  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  427 

account  of  the  difficulty  of  finding  the  mean  epochs  of  observation,  and  also  from  the 
fact  that  Bessel  has  applied  the  correction,  approximately,  by  comparison  with  Po  1800. 

In  Dr.  Bruhnt?  reduction  of  Gradmessung  stars  is  found  a  list  of  declinations 
which  have  been  computed  by  Dr.  Auwers  from  the  observations  of  Bradley.  But  these 
are  not  definitive,  nor  are  they  at  this  stage  of  their  reduction  independent,  because 
Bessel's  (Konigsberg)  refractions  have  been  employed.  It  will  be  seen  that  the  weight 
of  testimony  is  in  favor  of  refractions,  on  the  average,  at  least  as  small  as  those  which 
Bessel  deduced  from  Bradley's  observations.  Professor  Newcomb  kindly  placed  at  my 
disposal  similar  results  for  a  limited  list  of  stars  which  he  was  reducing.  But  both  the 
lists  combined  embrace  less  than  half  the  stars  required  in  this  discussion,  so  that  the 
old  results  were  used. 

Po  1800.  I  have  applied  correction  to  this  catalogue  only  for  proper  motion  in  a  few 
cases  where  the  latter  is  large.  The  effect  of  the  nutation  correction  is  included  in  the 
A.  R.  term  of  the  declination  correction  subsequently  ascertained. 

Bh  10.  The  mean  epochs  of  observation  are  secured  from  the  first  Radcliffe  cata- 
logue, and  the  proper  motion  correction  applied  iu  every  case.  As  the  catalogue  was 
not  included  iu  Class  I.,  the  application  of  nutation  correction  was  not  made,  but  it  is 
included  in  the  A.  R.  term  subsequently  found. 

In  the  use  of  this  catalogue  I  have  encountered  a  difficulty  which  introduces  some 
uncertainty  iu  the  results.  For  many  of  the  stars  most  frequently  observed  two  results 
for  declination  are  given  iu  the  catalogue.  In  the  introduction  this  is  explaiued  by  say- 
ing that  the  first  of  the  two  results  was  originally  reduced  to  1807,  and  the  second  to 
1812.  I  have  assumed  that  the  observations  are  distinct,  and  that  the  epoch  given  for 
these  stars  in  Re  45  is  the  epoch  of  the  first  set.  In  all  these  cases  the  mean  of  the 
two  results  has  been  taken,  without  correction  for  proper  motion,  as  the  mean  epoch  is 
probably  very  near  1810. 

The  history  of  the  reductions,  for  reasons  partly  unavoidable,  is  an  unfortunate  one, 
and  this  is  the  more  to  bo  regretted,  for  the  editor  says  (p.  ix,  Int.),  "There  can  be  no 
doubt,  I  conceive,  that  this  instrument  at  the  time  of  its  erection,  and  for  several  years 
afterward,  was  the  finest  in  the  world."  It  appears  to  have  been  well  handled,  and  was 
reversed  ten  times  at  least  during  the  active  period  of  the  observations  making  up  this 
catalogue.  The  materials  were  probably  suited  to  the  formation  of  an  independent  cat- 
alogue, which  would  have  been  no  mean  contribution  to  the  solution  of  the  problem  of 
absolute  declinations. 

Kg  21.  To  the  results  as  given  by  Dollen  has  been  applied  the  correction  —  ".24 
sin  (a  +  7°.5),  duo  to  the  use  of  Lindenan's  nutation. 

Gh  22.  The  correction  —  ".'2'J  sin  (a  +  32°.l)  is  applied  for  nutation. 

Dt  24.  No  correction  is  applied  to  this  catalogue. 

Ao  29.  Correction  for  Lindenau's  nutation  +  ".24  sin  (a  —  9Q.3),  is  adopted. 

Va  29.  The  same  nutation  correction  as  for  Ao  29  is  used. 

The  observations  are  reduced  with  Bessel's  Kb'uigsberg  refractions,  but  no  details 
are  given  whereby  an  independent  judgment  may  be  formed  of  the  character  and  accu- 
racy of  the  declinations. 

Dt  30.  To  all  the  results  have  been  applied  "  Correctiones  Ultimas"  (Pos.  Med.,  pp. 
351  to  371),  which  is  considered  as  bringing  them  systematically  in  accordance  with 
those  of  Dt  24.  It  may  be  doubted  whether  this  is  completely  accomplished  for  the 


428 


UNITED  STATES  NOKTHERN  BOUNDARY  COMMISSION. 


[22] 


entire  series,  aud  so  this  catalogue  has  not  beeu  used  in  formation  of  Normal  System. 
Wherever  the  proper  motions  have  not  beeu  ascertained  by  comparison  with  Fund. 
Ast.  this  correction  has  been  applied,  using  for  the  purpose  the  mean  date  of  observa- 
tion, always  supplied  in  such  cases  iu  the  Catalogus  Generalis. 

S.  H.  31.  The  observations  were  reduced  with  Young's  refractions.  This  table  is 
given  in  the  introduction,  p.  22,  for  "adapting  the  St.  Helena  declinations  to  Bessel's 
refractions." 


a 

Correction. 

t 

Correction. 

'    o 

a 

o 

a 

—  85. 

0.0 

+    5 

+  1.4 

—  75 

+    -4 

+  15 

+  1.5 

—  65 

+     .6 

+  25 

+  1.6 

—  55 

+     .* 

+  35 

+  1.8 

—  45 

+    .9 

+  45 

+  2.0 

—  35 

+  1.0 

+  50 

+  2.2 

—  25 

+  1.1 

+  55 

+  2.4 

—  15 

+  1.2 

+  60 

+  2.6 

—    5 

+  1.3 

+  65 

+  2.2 

+    5 

+  1.4 

These  corrections  are  applied  at  the  outset  to  all  the  declinations.  The  position 
of  the  observatory  (<p  =  —  15°  55')  does  not  admit  of  a  determination  of  the  refraction 
by  observations  of  circum polar  stars.  A  considerable  number  of  catalogues  of  northern 
observatories,  which  are  based  upon  Bessel's  refractions,  have  been  admitted  into  Class 
I.  (see  p.  14),  and  it  is  likely  that  errors  nrising  from  that  course  will  be  counteracted  to 
some  extent  by  the  adoption  of  the  same  refractions  for  the  observations  of  the  southern 
hemisphere.  The  results  are  reduced  to  the  nearest  tenth  of  seconds,  and  when  these 
are  corrected  for  refraction  the  declinations  may  be  in  error,  from  neglect  of  hnndredths, 
nearly  a  tenth  of  a  second.  I  have,  therefore,  neglected  the  small  nutation  correc- 
tion, aud,  except  in  a  few  extreme  cases,  that  for  proper  motion.  The  effect  of  nutation 
correction  is,  however,  included  in  the  A.  E.  term  found  in  the  discussion  of  systematic 
correction. 

Gh  30.  The  employment  of  Bradley's  refractions,  the  variety  of  practice  in  reduc 
tion  of  declinations  from  apparent  to  mean  place,  and  the  difficulty  in  searching  out 
the  mean  epoch  of  observation  for  each  star,  have  led  me  to  neglect  all  corrections  and 
to  use  the  catalogue  places  unchanged.  Dr.  Auwers*  has  briefly  and  conclusively  shown 
that  a  new  reduction  of  this  beautiful  series  of  observations  is  desirable. 

C.  G.  H.  31.  The  nutation  correction  is  +  ".23  sin  (a  +  200.3).  The  observations 
are  reduced  with  the  latitude  subsequently  found  by  Henderson.  The  results  are  few 
and  of  small  weight,  but  their  important  bearing  on  the  declinations  of  stars  in  the 
southern  hemisphere  has  led  to  their  use. 

C.  G.  H.  33.  The  constant  of  nutation  used  iu  this  series  is  that  of  the  A.  S.  C., 
9".25.  The  observations  were  reduced  to  1833,  ©  =  281°.  The  total  correction  for  both 
causes  is  —  ".07  sin  (a  +  81°.5).  The  observations  are  very  carefully  reduced  aud 
discussed;  and,  as  far  as  possible,  with  anon-reversible  instrument,  the  methods  of 
Bessel  (Kon.  Beob.  Bd.  vii,  and  Ast.  Nuch.  73)  were  followed  by  Henderson.  Strictly 
*  Publications  of  tha  Antronomisdic  GcseUschaft  (II.).  Dr.  Auwers's  paper  on  the  proper  motion  of  Sirius. 


[23J 


ItEPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


429 


speaking,  however,  this  series  does  not  give  independent  determinations;  for  the  correc- 
tions for  flexure  from  reflection  observations,  and  for  refraction  from  observations  of 
circumpolar  stars,  are  rejected  on  the  authority  of  comparisons  made  with  the  results 
obtained  by  Bessol,  Struve,  and  Airy,  at  northern  observatories.  A  defect  in  the 
instrument  by  which  the  readings  of  separate  microscopes  are  made  to  differ  very 
greatly,  is  exhaustively  discussed  by  Sir  George  B.  Airy  and  others  (vol.  viii,  Mem.  R. 
A.  S.,  etc.),  and  assurance  is  given  that  the  mean  of  six  microscopes  is  free  from  seri- 
ous error.  This  appears  to  be  confirmed  by  the  small  probable  error  ±  ".23  for  mean 
of  an  infinite  number  of  observations  found  by  Henderson.  The  precision  of  the  indi- 
vidual observations,  all  made  by  Henderson  in  person,  has  seldom  been  excelled  in 
work  of  this  kind. 

Mh  34.  The  nutation  correction  is  +  ".18  sin  (a  +  82°).  The  declinations  as  given 
in  vol.  xx,  Munich  Obs.,  are  combined  into  single  results  according  to  the  number  of 
observations  in  each  year  from  1829  to  1840.  lu  deducing  systematic  corrections,  the 
numbers  in  column  "B  —  i"in  the  tables  preceding  the  observations  for  1833  and 
1834  (in  Obs.  Astr.  in  Spec.  Reg.  Mon.}  are  used.  These  are  corrections  to  Bessel's 
declinations  (Tab.  Reg.)  given  by  Lament's  observations  of  fundamental  stars;  but 
I  have  not  used  them  in  discussing  the  places  of  the  fundamental  stars. 

CAMBRIDGE  ANNUAL  CATALOGUES. 

Ce  34.  The  annual  catalogues  at  Cambridge  for  many  years  were  constructed  by 
the  aid  of  the  proper  motions  and  constants  of  the  Ast.  Soc.  Catalogue  (Baily  1830), 
with  the  day  numbers  of  Nautical  Almanac.  By  use  of  Nautical  Almanacs  previous 
to  1857,  stars  are  reduced  with  nutation  9".25,  to  "Jan.  1,"  instead  of  ©  =  280°.  Both 
corrections,  with  the  small  correction  for  precession  of  A.  S.  C.,  can  be  combined  in 
one  formula.  The  following  list  of  corrections  will  serve  for  this  and  other  series 
shortly  to  be  mentioned. 


Year. 

Correction  for  nutation, 
epoch,  and  precession. 

Year. 

Correction  for  nntation, 
epoch,  and  precession. 

//                        o 

/'                                  O 

1833 

+  .  08  sin  (o  4-  265) 

1841 

4-  .05  sin  (o  4-  289) 

1834 

-j-  .07  sin  (a  +  272) 

1842 

+  .04  sin  («  4-  284) 

1835 

4-  .  06  sin  (a  -j-  276) 

1843 

4-  .  02  sin  (a  +  270) 

1836 

-j-  .  04  sin  (a  -j-  293) 

1844 

4-  .01  sin  (a  4-  227) 

1837 

4-  .  08  sin  (a  +  28?  ) 

1845 

+  .  05  sin  (a  +  254) 

1838 

+  .06  sin  (o  +  294) 

1846 

4-  .05  sin  (a  4-  245) 

1839 

4-  .  04  sin  (a  +  305) 

1847 

4-  .05  sin  (a  -j-  237) 

1840 

+  .  03  sin  (a  4-  322) 

These  corrections  are  entirely  unimportant,  and  the  neglect  of  them  would  have 
produced  no  serious  consequences.  The  correction  for  proper  motion  is,  however, 
often  considerable.  But  few  proper  motions  are  given  in  A.  S.  C.,  and  some  of  these 
few  are  very  far  from  the  truth.  The  approximate  mean  epochs  of  observation  f  T  all 
stars  for  which  the  latter  correction  is  more  than  ".02  or  ".03  were  examined  and  the 
corrections  carefully  applied.  The  barometer  used  in  1833-1835  gave  readings  .1  in. 
too  small.  This  error  was  disregarded  in  1833  and  1834.  Among  the  errata  in  the 


430 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[24J 


volume  for  1835  a  table  is  given,  which  serves  to  correct  north  polar  distances  to  the 
values  they  would  have  had  if  the  barometer  had  given  the  correct  readings.  The 
table  with  changed  signs,  to  make  it  applicable  to  declinations,  is  here  given : — 


<5 

Correction. 

,! 

Correction. 

6 

Correction. 

o 

// 

c 

// 

0 

// 

50  S.  P. 

—  .73 

+  80 

—  .05 

+  30 

—    .23 

CO  S.P. 

—  .32 

70 

—  .09 

+  20 

—    .27 

70  S.P. 

—  .16 

CO 

—  .13 

+  10 

—    .33 

80  S.P. 

—  .08 

50 

—  .10 

—  00 

—    .40 

+  90 

00 

+  40 

—  .19 

—  10 

—     .52 

—  20 

—    .75 

—  30 

-1.50 

These  corrections  were  applied  to  all  declinations  of  1833  and  1834. 

The  peculiar  feature  of  the  entire  Cambridge  series  is  the  frequency  of  reflection 
observations.  Within  the  limits  of  zenith  distance  where  they  are  practicable,  their 
number  is  generally  equal  to  those  taken  directly,  the  practice  being  to  observe  both 
at  the  same  transit.  The  discordance,  which  is  large,  is  divided  equally  between  the 
two  classes  of  observations.  The  position  of  the  telescope  was  frequently  changed 
on  the  circle — two  or  three  times  each  year  in  the  first  three  years,  afterward  at  the 
beginning  of  each  year  with  considerable  regularity  until  1852,  and  less  frequently 
after  that. 

At  this  observatory  the  experiment  was  tried  of  measuring  flexure  in  different 
zenith  distances  with  the  help  of  movable  collimators.  An  abstract  of  the  results  is 
printed  in  Gould's  Astronomical  Journal,  vol.  v,  p.  28.  The  correction  for  flexure 
determined  in  this  way  is  much  smaller  than  one-half  the  discordance  between  direct 
and  reflected  observations,  and  its  form  bears  little  resemblance  to  the  latter.  There 
can  be  little  doubt  that  a  portion  of  the  discordance  is  due  to  the  unequally  heated  air 
of  the  observing-room ;  a  consideration  which  serves  to  modify  the  weight  which  this 
series  might  otherwise  have  had  in  forming  the  normal  system. 

In  the  annual  catalogues  the  results  for  declination  are  given  separately  for  direct, 
reflected,  above  and  below  pole.  In  combining,  I  have  given  equal  weight  to  the  two 
classes  of  observations,  direct  and  reflected,  and  have  [used  no  observations  of  stars 
beyond  70°  zenith  distance  below  the  pole.  To  CO0  zenith  distance  equal  weights  are 
assigned ;  provided  in  each  case  eight  or  more  observations  were  given.  In  the  few 
cases  where  the  number  of  observations  is  smaller  and  quite  unequal,  weights  nearly 
in  proportion  to  the  square  root  of  the  number  of  observations  are  given.  At  C5° 
zenith  distance  determinations  below  the  pole  receive  weight  f,  and  at  70°,  |.  This 
practice  is  adhered  to  throughout  the  series. 

For  the  years  1833,  '34,  '35,  in  order  to  avoid  errors  which  would  arise  from  sys- 
tematic differences,  the  results  of  separate  years  are  combined  with  equal  weights, 
unless  the  discrepancy  in  the  number  of  observations  was  great  and  the  smaller  num- 
ber less  than  5,  when  arbitrary  weights  are  assigned. 

These  observations  have  been  combined  in  a  single  catalogue*  by  Sir  George  B. 


*  "A  catalogue  of  726  stars,  deduced  from  the  observations  made  at  the  Cambridge  observatory, 
from  1828  to  1835;  reduced  to  'Jan.  1,'  1830,  by  Geo.  Biddell  Airy,"  etc. 


[25J 


EEPOET  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


431 


Airy,  iu  Mem.  E.  A.  S.,  vol.  ii.  Tbc  proper  motions  of  A.  S.  C.  were  used  by  him,  and 
the  determinations  of  different  years  combined  with  weights  proportioned  to  the  number 
of  observations.  The  possible  error  from  these  sources  may  be  considerable;  and  the 
labor  of  constructing  anew  the  particular  places  desired,  though  much  greater  than 
would  have  arisen  from  the  correction  of  the  catalogue  for  proper  motion,  is  probably 
worth  tbe  while. 

Ce  40.  The  corrections  for  nutation,  epoch,  and  precession  are  given  above  under 
Ce  34.  No  proper  motions  were  used  in  reduction  except  those  of  the  Nautical  Alma- 
nac. In  volume  for  1838  u  new  co-latitude  is  given  derived  from  observations  of 
1837  and  1838.  The  correction  to  that  used  in  previous  years  is  +  ".09;  therefore  to 
the  declinations  above  pole  of  1836  and  1837  the  constant  correction  —  ".09  has  been 
added,  after  which  no  correction  is  required.  In  order  to  form  a  judgment  as  to  the 
individual  accuracy  of  the  declinations,  the  probable  error  is  computed  from  a  few 
of  the  stars  most  frequently  observed  within  40°  zenith  distance. 

In  1837     .......    284  residuals  (dir.)  gave  ±  ".59 

283  residuals  (ref.)  gave  ±  ".GO 

In  1840-'43 511  (dir.) ±  ".52 

509  (ref.)  .....  ±".55 

The  mean  ±  .56  is  considered  as  the  probable  error  of  a  single  pointing.  A  com- 
parison of  observations  made  in  different  years  gives  for  the  minimum  error  of  a  single 
position  ±  .20.  The  minimum  for  a  single  year  for  stars  observed,  both  directly  and 
by  reflection,  would  be  ±  .14.  These  results  are  apparently  too  small.  The  argument 
for  using  the  accompanying  table  of  weights  is  one-half  the  total  number  of  observa- 
tions in  any  one  year ;  and  it  supposes  that  the  probable  error  of  any  star,  circumpo- 
lars  excepted,  cannot  be  less  than  ±  .14.  It  can  only  be  considered  a  rough  approx- 
imation to  the  true  weights. 


wt. 

Number  of  obser- 
vations. 

Wt. 

Number  of  obser- 
vations. 

Wt. 

Number  of  obser- 
vations. 

1 

1 

6 

8  and  9 

11 

26  to  34 

2 

o 

7 

10  to  12 

12 

35  to  44 

3 

3  anil  4 

8 

13  to  15 

13 

45  to  61 

4 

5 

9 

16  to  20 

14 

62,  or  more. 

5 

6  and? 

10 

21  to  25 

The  probable  error  of  the  unit  is  thus  supposed  to  be  about  ±  .45,  iu  the  average 
of  cases.  With  these  weights,  the  residuals  formed  by  subtracting  the  assumed  dec- 
lination from  the  corrected  value  for  each  year,  are  formed  into  a  single  correction  to 
assumed  place. 

The  uumeroMS  errata  in  these  and  subsequent  years  are  carefully  applied. 

Ce  48.  In  1844  a  few  nadir  observations  had  been  taken  for  practice;  and  the 
method  was  adopted  for  obtaining  zenith  points  in  1845  and  subsequent  years.  It 
was,  however,  controlled  by  the  results  of  direct  and  reflected  observations.  In  1846 
began  the  use  of  the  a',  &',  c',  and  d'  of  the  B.  A.  C.  In  other  respects  the  observa- 
tions are  not  different  from  those  of  previous  years.  The  long  period  of  time,  how- 
ever, rendered  these  somewhat  arbitrary  divisions  necessary. 


432 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[2GJ 


These  corrections  for  nutation,  etc.,  are  applied  in  respective  years: — 


1845  +  ".05  sin  (a  +  254°) 

1846  +  ".05  sin  (a  +  245°) 

1847  +  ".05  sin  (a  +  231°) 

1848  +  ".03  sin  (a  +  214°) 


1849  +  ".07  siu  (a  +  2510) 

1850  +  ".06  siu  (a  +  253°) 

1851  +  ".05  sin  (a  +  25GQ) 


Inspection  of  the  observations  of  circumpolar  stars  indicate  that  a  considerable 
correction  for  latitude  is  needed.  Observations  of  <z  and  S  Ursa}  Minoris  are  alone 
available  for  ascertaining  this  correction.  The  table  of  weights  given  under  Ce  40  is 
used,  and  reflected  as  well  as  direct  observations  included.  Following  is  the  sum- 
mary : — 


Corrections  to  as- 
sumed latitude. 

Weight. 

Corrections  to  as- 
sumed latitude. 

Weight. 

1845 

—  .26 

5 

1851 

—  .32 

G 

1846 

—  .32 

8 

1847 

—  .30 

11 

(Dir.)... 

—  .52 

21 

1848 

—  .76 

4 

(Kef.)... 

—  .34 

20 

1849 

94 

j 

1850 

—  .73 

6 

Mean  .  . 

-  .43    ±.04 

Probable  error  of  unit  of  weight  ±  ".56. 

The  correction  —  ".43  is  applied  to  all  the  declinations  of  this  group.  This  steady 
diminution  in  values  of  latitude  obtained  since  1833  with  the  same  instrument,  used 
substantially  in  the  same  method,  is  suggestive  of  an  actual  change  in  that  element 
when  it  is  taken  in  connection  with  the  apparent  existence  of  the  like  phenomenon  at 
Greenwich,  Washington,  Poulkova,  and  elsewhere.* 

Ce  56.  During  this  period  there  is  a  marked  falling  off  both  in  the  number  and 
character  of  the  observations.  These  corrections  for  nutation  and  epoch  have  been 
employed : — 

1852  +  ".04  sin  (a  +  265°) 

1853  +  ".08  sin  [a  +  274°) 

1854  +  ".06  sin  (a  +  282°) 

1855  +  ".05  sin  (a  +  294°) 

1856  +  ".04  sin  (a  +  313°) 

As  in  preceding  years,  only  the  proper  motions  of  the  Nautical  Almanac  were  used 
in  the  annual  catalogues.  The  position  of  the  telescope  on  the  circle  was  changed  at 
irregular  intervals,  but  the  same  relative  weights  and  system  of  combining,  as  in  Ce 
40  and  Ce  48,  are  here  employed.  As  this  series  is  not  used  in  forming  the  Normal 
System,  no  correction  for  error  of  assumed  latitude  is  applied,  nor  do  the  observations 
themselves  afford  adequate  means  for  deducing  such  a  correction  independently.  The 
erratum  to  reflected  observations  of  1854  is  important. 

Ms  35.  The  results  from  this  catalogue  are  used  without  charge.    The  proper 


*  "  Die  Polhohe  von  Pulkowa.   Von  Dr.  Magnus  Nyre'n." 
and  60  of  this  paper. 


St.  Petersburg,  1873.    See  also  pp.  36 


[27]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  433 

motion  correction  is  often  large,  but  it  is  not  always  easy  to  find  out  whether  it  ought 
to  be  applied,  and  the  mean  date  of  observation  will  often  be  very  inexact.  The  weight 
of  these  observations  is  so  small  that  I  have  not  thought  it  worth  while  to  construct 
places  anew  from  the  special  catalogues  by  the  help  of  division  corrections  on  pp.  ccxix 
and  ccxx,  vol.  v. 

Ms  50.  The  declinations  require  the  full  amount  of  the  correction  for  proper 
motion,  but  this  is  usually  small,  owing  to  the  small  difference  between  epoch  of 
observation  and  that  of  reduction. 

EDINBURGH  ANNUAX,  CATALOGUES. 

Eh  37.  The  methods  of  reduction  to  apparent  place  are,  with  few  exceptions,  those 
employed  at  Cambridge  in  the  corresponding  years,  so  that  the  same  corrections  have 
been  applied.  The  position  of  the  telescope  on  the  circle  was  moved  at  the  beginning 
of  1839,  and  yearly,  afterward,  during  the  directorship  of  Henderson.  Strictly  speak- 
ing, only  the  observations  of  1834-5,  in  volume  I.,  are  independent,  and  the  succeeding 
catalogues  as  reduced  by  Henderson  depend  upon  this  first  one.  Ivory's  refractions  are 
employed  throughout  the  catalogues  composing  Eh  37,  so  that  in  this  respect  the  series 
is  not  independent.  The  discordance  in  1834-'35,  between  direct  and  reflected  obser- 
vations, is  quite  large,  and  the  latter  are  rejected  by  Henderson  in  making  up  the  decli- 
nations. The  corrections  derived  from  sun  observations  in  the  different  years  are  in 
the  mean  small,  and  furnish  tolerable  assurance  that  the  declinations  will  be  found 
quite  free  from  systematic  error.  All  determinations  of  the  same  star,  up  to  1839, 
I  have  combined  with  weights  proportional  to  the  number  of  observations.  This  result 
is  then  combined  with  that  for  1839,  on  the  supposition  that  the  minimum  error  in 
each  case  is  equal,  and  one-half  the  error  of  a  single  pointing.  This  was  an  over- 
sight, for  previous  to  1837.  in  most  observations,  six  microscopes  were  used ;  after  that 
only  two,  so  that  for  the  first  series  the  minimum  error  might  have  been  taken  about 
one-fourth  the  error  of  pointing.  However,  no  serious  error  has  arisen  from  this  cause. 

Henderson  estimates  (1839)  the  probable  error  of  pointing  at  ±  .5,  and  probable 
division  error,  when  mean  of  two  microscopes  is  taken,  ±  .3.  For  the  former  quantity 
I  have  found,  from  a  rough  trial,  ±  ".C.  It  will  be  seen  in  the  latitude  discussion  of 
Eh  43  that,  if  error  of  pointing  is  assumed  to  be  twice  the  minimum  error,  we  have  for 
the  former  ±  ".59,  and  for  the  latter  ±  ".29,  in  close  agreement  with  above  estimates. 
It  is  difficult  to  believe  that  the  minimum  error,  under  the  circumstances,  can  be  so 
small,  and  doubtless  a  more  rigorous  determination  of  probable  error  of  pointing  would 
show  that  to  be  slightly  smaller,  and  the  minimum  error  would  then  result  in  a  larger 
quantity. 

The  catalogue  for  1840  cannot  properly  be  classed  either  with  those  preceding  or 
following  it,  and  no  use  is  made  of  its  declinations. 

Eh  43.  The  observations  of  this  series  were  reduced  by  Professor  Smyth.  During 
the  entire  period  the  zenith  points  were  derived  from  nadir  observations,  a  practice 
begun  in  1841.  The  observations  in  1841-'2-'3  were  reduced  with  Bessel's  refractions, 
and  the  help  of  Nautical  Almanac  and  A.  S.  C.  In  1844  the  Nautical  Almanac  was 
used  with  the  constants  and  proper  motions  of  British  Association  Catalogue.  The 
corrections  to  first  three  years  for  nut.,  etc.,  are  taken  from  the  corresponding  formula? 
for  Cambridge.  For  1844  the  correction  is  insignificant. 
N  B 28 


434 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[28] 


In  reducing  from  the  mean  of  two  microscopes  to  the  mean  of  six,  Professor  Smyth 
continued  to  use  the  results  of  the  investigation  made  by  Henderson  (vol.  I.,  p.  vii,  et 
seq.).  As  the  telescope  was  clamped  to  a  different  part  of  the  circle  in  each  year,  it  is 
evident  that  any  considerable  error  in  the  formula?  01  correction  would  show  itself  in 
the  difference  between  the  declinations  of  the  same  star  in  different  years,  and  also  in 
the  latitudes  deduced  from  observations  of  circumpolar  stars.  Fortunately,  in  each  of 
the  years  there  are  a  considerable  number  of  the  latter  well  suited  to  the  examination 
of  this  question.  In  Ast.  Nacli.  Bd.  65,  s.  195,  by  Dr.  Auwers,  and  in  Bonn.  Bcob. 
Bd.  VII.,  Theil  II.,  s.  251,  by  Dr.  Argelander,  we  have  the  results  of  such  an  examin- 
ation. They  are  exhibited  in  the  fol'owing  table: — 


Cn      jtion  to  assumed  latitude  given 

by  observations  of  each  year. 

Year. 

Anwers. 

Argelander. 

1841 

—     .  20 

-  -    .  20 

1844 

—    .95 

-     .96 

1843 

+  1.44 

+  1.44 

1844 

17 

.15 

Both  Auwers  and  Argelander  use  these  as  constant  corrections  to  the  declinations 
of  respective  years.  The  latter  says,  "  Wie  diese  grossen  Vershiedenheiten  zu  erklaren 
sind,  weiss  ich  nicht  zu  deuten.  Theilungsfehler  an  dem  Orte  des  Sterns  kounen  es 
nnmoglioh  sein. ;  dagegen  streitet  die  nahe  Uebereiustimmung  bei  alien  vershiedenen 
Sternen,  und  besouders  auch  der  Uiustand,  dass  die  Untershiede  auch  bei  dem  Polar- 
Sterne  sich  zeigen,  bei  dem  die  Puncte  des  Kreises  fur  die  OC.  und  UC.  nur  3°  ausein- 
ander  liegen.  Man  erhiilt  aber  1842  aus  resp.  76  und  64  Beobachtungen  UO. — OC. 
—  2".5,  im  Jahrc  1843  aus  48  und  42  Beobachtungen  +  3".l.  Man  muss  also  den  Feh- 
ler  wohl  in  der  Bestitnmung  des  Nadirpuuctes  suchen,  aber  auch  hier  kann  man  ihn 
durch  Theiluugsfehler  allein  schwerlich  erklaren.  Es  hiesse  dies  voraussetzen,  dass 
bei  einem  6fussigen  Kreise  von  Troughton  und  Simms  tier  Theilungsfehler  des  Kreises 
an  zwei  Puncten  desselbeu  um  2".4  verschieden  wiire,  was  wohl  Niemand,  der  die  aus- 
gezeichneteu  Leistuugen  dieser  Kiinstler  kennt,  fur  moglich  halten  wird  *  *  *  * 
so  kann  man  die  grossen  Unterschiede  iiur  dem  ungliicklichen  Zusarnmentreflen  meh- 
rerer  Ursachen  zuschreiben." 

An  examination  of  the  declinations  near  the  equator  shows  that  to  apply  these 
constant  differences  will,  for  this  region,  in  some  cases,  produce  greater  systematic  dis- 
cordance than  existed  before.  In  view  of  all  the  arguments  so  strongly  put  by  Arge- 
lander, there  appeared  to  be  but  one  available  hypothesis  by  the  adoption  of  which  the 
difficulty  could  be  satisfactorily  solved.  The  reduction  for  division  error  actually  used 
is  supposed  to  be  inapplicable,  and  an  attempt  is  made  to  deduce  a  new  one  from  a 
comparison  of  the  observations  of  the  same  stars  in  different  years.  Granting  the  cor- 
rectness of  the  reduction  from  two  microscopes  to  six,  as  found  by  Henderson  (vol.  i), 
we  may  easily  conceive  such  changes  to  have  taken  place  in  the  instrument  that  these, 
combined  with  small  errors  in  zenithal  divisions  and  the  possible  error  of  the  mean 


[29]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          435 

reading  of  six  microscopes,  may  have  caused  the  discrepancies  actually  found.  The 
arrangement  of  the  observations  is  tolerably  favorable  to  this  undertaking.  The  circle 
readings  increase  from  the  pole  toward  the  equator,  and  for  the  zenith  were: — 

1841  590  58' 

1842  340  08' 

1843  79°  05' 

1844  1390  05' 

The  effect  of  the  corrections  actually  applied  to  nadirs  and  zenith  distances  of 
stars  is  first  subtracted  from  the  declinations.  For  that  purpose  the  table  of  division 
corrections  in  the  introduction  to  each  volume  is  used.  We  now  have  the  declina- 
tions as  they  would  have  resulted  had  no  correction  for  division  been  applied.  It  is 
possible  thyt  an  important  part  of  the  discrepancies  may  have  been  caused  by  flex- 
ure of  the  circle,  but  not  likely.  If  such  is  the  case,  it  cannot  well  be  determined 
from  the  data  furnished  by  the  observations.  It  is  therefore  assumed  that  the  diffi- 
culty is  due  to  division  error.  The  mean  of  two  microscopes  may  be  affected  by  errors 
requiring  corrections  of  the  form: — 

x  sin  2  U  +  tf  cos  2  R  +  x"  sin  4  R  +  x"'  cos  4  R  +  &c. 

The  coefficients  x  and  a^,  only,  have  been  determined ;  which  is  perhaps  to  be  regretted. 
The  effect  of  accidental  errors  of  the  nadir  divisions  has  also  been  included.  The  fol- 
lowing notation  is  adopted: — 

5  =  Declination  as  printed  in  annual  catalogues,  but  referred  to  1843,  and 

corrected  by  the  requisite  amounts  for  nutation  and  proper  motion. 

R  =  Circle  reading  for  a  given  declination. 

R1  =  Nadir  reading  for  the  same. 

It  and  k'       =  Division  corrections  actually  applied  to  R  and  R1. 

x  and  x1       =  Coefficients  of  division  correction  as  explained  above. 

0i)  "2,  03>  *>4,  =  Correction  to  nadir  divisions  respectively  of  1841, 1842,  1843,  and  1844, 
for  accidental  error,  or  deviation  from  the  law  expressed  by  x  sin  2  R 
+  x1  cos  2  R. 

A  <f  =  Correction  to  assumed  latitude,  y>. 

The  application  of  any  of  the  above  quantities  is  restricted  to  a  given  year  by  the 
use  of  subscript  figures,  1,  2,  3  and  4,  respectively  for  1841, 1842,  1843,  and  1844.  The 
declinations  are  referred  to  the  common  epoch  1843.0  by  means  of  the  reduction  of 
assumed  places  (Section  III).  The  corrected  declination  will  then  be: — 

(1)  R'  +  I'  +  180°  +  <f—  R  —  1c  +  x  (sin  2  R'  —  sin  2  R)  +  x'(ccs  2  R'  —  cos  2  R) 

+  v  +  A  <f 
We  shall  then  have: — 

(2)  0  =  (<?!  -  k't,  +  ki)  —  (<52  —  k'2  +  fc2)  +  x  (sin  2  R't  -  sin  2  R'2) 
+  x'  (cos  2  R\  —  cos  2  R'z)  +  vl  —  v2  +  x  (sin  2  R2  —  sin  2  R^ 

+  x'  (cos  2  Rz  —  cos  2  RI). 

The  comparison  for  any  other  years  may  be  derived  from  this  by  the  substitution 
of  the  required  figures  in  subscript.  For  convenience,  the  comparison  was  confined  to 
stars  of  the  provisional  catalogue  and  to  those  north  of  10°  south  declination. 


436  UNITED  STATES  NOETHEEN  BOUNDAEY  COMMISSION.  [30 1 

It  is  evident  that  «i,  v2,  v3,  and  vt,  cannot  be  absolutely  determined  with  the  data 
proposed.  It  will  be  necessary  to  assume : — 

and  to  express  t'4  in  terms  of  the  other  three  quantities.  This  will  not  affect  the  decli- 
nations ;  but  will  produce  an  error  in  the  latitude  of  one-fourth  the  sum  of  the  quan- 
tities in  question. 

Every  combination  of  differences  that  could  be  made  was  used.  Thus,  a  declina- 
tion observed  in  three  years  furnished  throe  differences;  and  four  years,  six.  There 
were  very  few  of  the  latter.  The  weights  are  assigned  on  the  supposition  that  a  dec- 
lination is  subject  to  a  constant  probable  error  which  is  equal  to  one-half  the  error  of 
pointing. 

Where  a  star  has  been  observed  in  three  years  there  are  but  two  independent  com- 
parisons; and  for  four  determinations  we  have  three  independent  comparisons.  In 
the  former  case,  each  of  the  three  equations  received  two-thirds  the  weight  it  otherwise 
would  have  had,  and  in  the  latter,  each  of  the  six  one-half.  The  unit  of  weight  is 
that  due  to  five  observations  in  each  of  two  years  where  there  is  but  one  comparison 
for  a  given  star.  It  was  found  that  the  computation  could  be  much  simplified,  without 
appreciable  error,  by  assuming  the  simple  scale  of  weights,  1.0,  .6,  and  .3. 

The  coefficients  were  computed  to  the  nearest  tenth  only  ;  but  the  equations  were 
not  grouped  in  the  solution.  There  were  in  all  307  equations  of  the  total  weight  188. 
Every  part  of  the  work  was  either  rigorously  checked  or  duplicated.  The  resulting 
normal  equations  are  these  : — 

+  257.4  V!  +    90.5 

+    90.5  vi  +  236.4 

+    74.9  vi  +  103.5 

+  152.2  vi  +  134.3 

—    10.7  Vi  +    62.5 ' 

The  solution  gives,  with  vt  =  —  Vi  —  v2  —  «3 

Henderson. 

Vi  =  —  ".11  x  =  —  ".664        (  —  ".100  ) 

i-t  =  -  ".21  a7  =  -  ".598         (  -  ".388  ) 

03  =  +  ".46 
r4  =  -  ".14 

The  differences  are  well  represented,  the  error  seldom  rising  as  high  as  ".3  in  the 
mean  of  a  zone  10°  wide.  The  probable  error  cannot  be  estimated  from  the  residuals. 
If  taken  from  them,  it  would  be  much  too  small.  Assuming  the  probable  error  found 
from  latitude  discussion,  that  of  the  unit  of  weight  would  be  ±  ".56  ;•  and  the  probable 
errors  of  x  and  x1  would  be  ±  ".04  each;  and  of  vit  »2,  etc.,  ±  ".06  each.  But  in  refer- 
ence to  the  latter,  it  must  bo  borne  in  mind  that  this  probable  error  is  that  of  the  rela- 
tive values,  and  that  their  common  probable  error  can  be  taken  roughly  at  ±  ".15;  so 
that  the  actual  probable  error  of  the  quantities  in  the  absolute  sense  is  about  ±  ".1C. 

Thus  the  values  of  the  zenithal  division  errors  are  reduced  to  quantities  of  not 
improbable  magnitude.  The  difference  between  .the  coefficients  of  x  and  x1  as  here 
determined,  and  as  determined  by  Henderson,  is  important. 


a 

+     74.9  V3     • 

f  152.2  x     —    10.7  x1 

4-  107.2    =  0 

+  103.5  v3 

-f-  134.3  x     +    62.5  X? 

•f  138.2    =  0 

+  187.6  r3 

4-    81.4  a?     -    57.7  a;' 

+    36.5    =  0 

+    81.4  v3 

4-  257.1  x    +    46.2  a' 

+  205.6    =  0 

-    57.7  v3    • 

f    46.2  x     +  260.2  x1 

4-  224.4    =  0 

[31] 


EEPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  437 


The  farther  correction  A  y>  is  required  before  the  declinations  can  be  regarded  as 
definitive.  The  discussion  of  A  <p  for  the  different  years  will  also  afford  a  good  test  of 
the  corrections  already  deduced. 

The  systematic  corrections  of  the  zenithal  divisions  are  respectively  —  ".19,  —  ".80, 
+  ".39  and  +  ".50  for  1841-2-3  and  4.  These  added  to  the  respective  corrections  for 
accidental  error,  and  k'  for  each  year,  give  the  following  corrections  to  the  declina- 
tions : — 

(1841)  -  ".38  +  ".894  sin  (2  B  +  48°)  +  fa 

(1842)  -  ".9G  +  ".894  sin  (2  B  +  48°)  +  lct 

(1843)  +  ".72  +  ".894  sin  (2  B  +  48°)  +  Jc3 

(1844)  +  ".18  +  "  894  sin  (2  B  +  48°)  +  fa 

Where  fa  etc.,  is  to  be  taken  for  each  star  from  the  table  p.  186,  volume  for  1841,  or 
from  the  succeeding  volumes.  These  corrections  are,  of  course,  to  be  applied  with 
opposite  signs  to  results  from  observations  of  lower  culmination. 

Each  year  furnishes  a  considerable  number  of  observations  suited  to  determina- 
tion of  latitude.  Except  for  a  and  S  Ursae  Minoris,  with  a  few  others,  three  observa- 
tions of  the  same  star  were  generally  made  in  each  culmination.  The  computation  is 
thus  practically  unaffected  by  the  question  of  relative  weights,  and  is  greatly  facilitated. 
Taking  three  observations  in  each  culmination  as  the  standard  unit  for2  A  y>,  weights 
were  computed  for  the  few  that  required  it  on  the  same  assumption  as  in  the  preceding 
portion  of  the  discussion.  The  latitude  observations  are  all  on  stars  of  declination 
greater  than  74°,  so  that  the  refraction  cannot  be  examined,  and  the  observations  may 
be  assumed  to  be  of  equal  accuracy  in  the  small  range  of  zenith  distance.  The  results 
are  these : — 


Year. 

A  <j, 

Number  of 
stars. 

Weight. 

it 

1841 
1842 
1843 
1844 

Mean  .  .  . 

—  .49  [±  .12] 
-  .15  [±  .11] 
+  .15  [±  .11] 
+  .04  [±  .12] 

18 
32 
31 
27 

50 
72 
69 
56 

—  .09  [±  .06] 

108 

247 

The  differences  are  not  much  greater  than  the  probable  errors  should  lead  us  to 
expect.  The  probable  error  of  the  unit  of  weight  calculated  from  the  108  residuals  is 
±  ".64.  This  gives  for  probable  error  of  pointing  ±  ".59,  and  for  minimum  probable 
error  i  ".29;  the  latter  is  in  close  agreement  with  the  value  ±  ".3  assumed  by  Hen- 
derson in  1839.  The  probable  errors  of  J  y>,  as  given  above,  take  into  account  the 
probable  error  of  the  formulae  derived  for  division  correction.  The  probable  error  of 
the  mean  value  of  A  <p  computed  from  the  residuals  is  ±  ".04.  All  the  values,  how- 
ever, are  subject  to  a  common  probable  error  of  about  ±  ".15,  besides  the  error  in 
adopted  refraction;  so  that,  absolutely  considered,  the  correction  to  the  assumed  lati- 
tude has  a  probable  error  not  far  from  ±  ".2.  Except  for  the  uncertainty  of  refraction 
this  increase  of  probable  error  is  without  influence  on  the  declinations.  The  quan- 
tity —  ".09  is  therefore  added  to  each  of  the  corrections  marked  (A),  and,  since  B  = 


438 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[32 1 


(B) 


E'  +  y>  —  d,  we  Lave  by  the  proper  substitutions,  the  following  corrections  to  the  decli- 
nations of  Eh  43,  as  printed  in  the  annual  catalogues : — 

(1841)  -       ".47  +  ".S94_(280°  —  2  8)  +  Jct 

(1842)  -  1".05  +  ".894  (228°  -  2  d)  +  k2 

(1843)  +     ".63  +  ".894  (218°  -25)+  7r3 

(1844)  +     ".09  +  ".894  (  78"  -  2  S)  +  7,-4 

where  Arj.  etc.,  are  to  be  taken,  as  before,  from  the  tables  of  division  correction  in  the 
annual  volumes. 

The  following  table  exhibits  in  column  I.  the  values  of  this  expression,  computea 
for  every  five  degrees  of  declination  (and  includes  ft).  Column  II.  is  the  sum  of  column 
I.  and  the  definitive  correction  found  for  Eh  43  in  Table  IX.  at  the  end  of  this  paper. 
To  this  is  still  to  be  added  a  small  correction  depending  on  right  ascension. 

Table  of  corrections  to  Edinburgh,  1841-1844. 


S 

1841. 

1842. 

1843. 

1844. 

I. 

II. 

I. 

II. 

I. 

II. 

I. 

II. 

S.P. 

0 

// 

// 

// 

// 

// 

a 

// 

// 

75 

+  .13 

+  .13 

+  1.24 

+  1.24 

—  1.37 

—  1.37 

+  .34 

+  .34 

SO 

+  .01 

+  .01 

+  1.16 

+  1.16 

—  1.39 

—  1.39 

+  .37 

+  .37 

85 

—  .17 

—  .17 

+  1.06 

+  1.08 

—  1.36 

—  1.36 

+  .37 

+  .37 

90 

—  .23 

—  .23 

+  .94 

+  .94 

—  1.29 

—  1.29 

+  .36 

+  .36 

Above  pole. 

+  90 

+  .23 

+  .23 

—  .94 

—  .94 

+  1.29 

+  1.29 

—  .36 

—  .36 

+  85 

+  .28 

+  .28 

—  .80 

—  .80 

+  1.18 

+  1.18 

—  .34 

—  .34 

+  80 

+  .28 

+  .28 

—  .67 

—  .67 

+  1.04 

+  1.04 

—  .31 

—  .31 

+  75 

+  .25 

+  .25 

—  .56 

—  .56 

+  ;90 

+  .90 

—  .28 

—  .28 

+  70 

+  .16 

+  .16 

—  .44 

—  .44 

+  .75 

+  .75 

—  .26 

-  .26 

+  05 

+  .05 

+  .03 

—  .36 

—  .38 

+  .59 

+  .57 

—  .24 

—  .26 

+  60 

—  .08 

—  .13 

—  .31 

—  .36 

+  .46 

+  .41 

—  .23 

—  .23 

+  55 

—  .23 

—  .31 

—  .30 

—  .38 

+  .35 

+  .27 

—  .23 

—  .31 

+  50 

—  .39 

—  .47 

—  .33 

—  .41 

+  .26 

+  .18 

—  .23 

—  .31 

+  45 

—  .54 

—  .60 

—  .40 

—  .46 

+  .20 

+  .14 

—  .21 

—  .£7 

+  40 

—  .67 

—  .70 

—  .51 

—  .54 

+  .17 

+  .14 

—  .20 

-  ,23 

+  35 

—  .78 

—  .78 

—  .65 

—  .65 

+  .13 

+  .18 

—  .16 

—  .16 

+  30 

—  .86 

—  .81 

—  .78 

—  .73 

+  .18 

+  .23 

—  .10 

—  .or. 

+  25 

-  .91 

—  .79 

—  .94 

—  .82 

+  .20 

+  .32 

—  .02 

+  .10 

+  20 

—  .93 

—  .74 

—  1.09 

—  .90 

+  .23 

+  .42 

+  .09 

+  .28 

+  15 

—  .93 

—  .66 

—  1.23 

—  .96 

+  .27 

+  .54 

+  .21 

+  .48 

+  10 

—  .92 

—  .58 

—  1.34 

—  1.00 

+  .28 

+  .62 

+  .34 

+  .68 

+  5 

—  .89 

—  .53 

—  1.43 

—  1.07 

+  .30 

+  .66 

+  .47 

+  .83 

0 

—  .87 

—  .53 

—  1.48 

—  1.14 

+  .31 

+  .65 

+  .59 

+  .93 

—  5 

—  .84 

—  .59 

—  1.51 

—  1.26 

+  .31 

+  .56 

+  .71 

+  .93 

—  10 

—  .82 

—  .  .69 

—  1.51 

—  1.38 

+  .32 

+  .45 

+  .79 

+  .92 

—  15 

—  .80 

—  .78 

—  1.50 

—  1.48 

+  .33 

+  .35 

+  .83 

+  .85 

—  20 

—  .80 

—  .88 

—  1.48 

—  1.56 

+  .35 

+  .27 

+  .83 

+  .75 

—  25 

—  .80 

—  .95 

—  1.46 

—  1.61 

+  .38 

+  .23 

+  .81 

+  .66 

—  30 

—  .79 

—1.00 

—  1.44 

—  1.65 

+  .45 

+  .24 

+  .74 

+  .53 

[33] 


HEPOET  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


439 


With  the  corrections  of  column  I.  added  to  those  for  nutation  and  proper  motion 
all  the  results  for  a  given  star  were  formed  into  a  single  mean,  with  the  following  table 
of  weights : — 


Weights. 

Observations. 

1 

1 

2 

2  a       3 

2.5 

4 

3 

5  to  9 

4 

10  to  35 

5 

36,  or  more. 

Eh  58,  Eh  63  and  Eh  67.  There  are  few  observations  in  this  series ;  but  many  of 
them  relate  to  stars  for  which  few  observations  are  found  elsewhere.  The  unimportant 
corrections  for  nutation  applied  to  Cambridge  annual  catalogues  of  corresponding 
years  previous  to  1857  are  used.  The  proper  motion  correction  is  generally  neg- 
lected :  the  difference  between  t'  oso  assumed  in  this  paper  and  those  of  B.  A.  0.  used 
in  reduction  of  Edinburgh  observations  being  usually  small,  for  the  short  interval  of 
time  intervening  between  the  mean  epoch  of  observation  and  the  beginning  of  the 
year.  The  grouping  is  determined  by  constancy  of  zenith  circle  readings,  which,  how- 
ever, were  often  changed  during  the  period  embraced  in  Eh  58. 

Kg  43.  The  reduction  by  Luther,  in  Ast.  Na^li.  1070,  employs  Bessel's  refractions 
(1821)  and  derives  the  latitude  from  a.  Urs.  Miu.,  a  Aurigao  andaCygni.  I  have  followed 
the  lead  of  Dr.  Auwers  (Ast.  Nacli.  1549),  talsic;;  the  latitude  from  a  Urs.  Min.  alone 
and  applying  the  correction  —  ".17  to  the  declinations  of  all  stars,  except  a  Auriga 
and  a  Cygni,  whose  declinations  are  taken  from  upper  culmination  alone,  and  the  cata- 
logue places  corrected  respectively  by  —  ".44  and  —  ".41.  Tho  observations  were 
originally  reduced  with  Peters's  nutation. 

GREENWICH  CATALOGUES,  1836-1672. 

This  long  and  valuable  series  of  observations  is  remarkable  for  the  uniformity  of 
its  plan  and  methods,  the  thoroughness  and  accuracy  of  its  numerical  reductions, 
and  the  vast  amount  of  material  it  contains,  chiefly  relating  to  places  of  sun,  moon, 
planets,  and  stars  of  the  sixth  magnitude,  or  brighter.  The  observations  are  made 
with  non  reversible  instruments,  and  the  problem  of  absolute  declinations  is  rendered 
altogether  subordinate  to  the  requirements  of  routine  work  on  a  large  number  of  ob- 
jects.* This  robs  the  series  oi  an  interest  it  might  otherwise  possess  ;  but  when  syste- 
matic corrections  to  its  various  catalogues  are  once  ascertained,  it  becomes  the  richest 
mine  of  information  on  the  ik  elinations  of  the  brighter  stars. 

Two  mural  circles  were  used  until  Marcb,  1839,  then  a  single  mural  circlet  until 
1851,  when  the  great  transit  circle  was  mounted,  and  has  been  used  until  the  present 
time.  The  position  of  the  telescope  on  each  of  Ihe  mural  circles  was  changed  at  the 
beginning  of  each  year.  The  relation  of  the  telescope  and  circle  of  the  transit  circle 
is  invariable. 

*  In  a  critical  examination  of  Greenwich  polar  distances  for  1851-1854  Mr.  A.  Marth  has  pointed 
out  very  conclusively  the  defects  of  the  Greenwich  transit  circle,  as  applied  to  the  problem  of  absolute 
declinations.  ( Ast.  Nach.,  12CiO.) 

t  In  1848,  for  a  short  time,  the  Jones  Cape  circle  was  used. 


440          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.  [34] 

The  observations  were  reduced  with  Bessel's  refractions  (Tab.  Reg.)  until  1868, 
when  tbe  refractions  of  the  Fwndamenta  multiplied  by  0.99797  were  adopted  on  the 
authority  of  a  discussion  by  Mr.  E.  J.  Stone  (Month.  Not.,  vol.  28,  p.  27),  who  uses  for 
tbe  purpose  observations  made  with  the  transit  circle  of  Greenwich  1857-1805. 

Gh  S9  and  Gh  45.  The  observations  of  separate  years  are  usually  reduced  to  the 
beginning  of  the  year  with  no  proper  motion,  or  with  values  of  that  element  taken 
from  A.  S.  C.  Wherever  the  error  from  this  is  considerable,  it  has  been  carefully 
attended  to  in  the  errata  of  later  catalogues.  1  have  not  investigated  any  cases  inde- 
pendently of  these.  The  proper  motions  of  the  B.  A.  C.  were  used  in  compiling  the 
general  from  the  special  catalogues.  Where  the  difference  between  these  and  those 
assumed  in  this  paper  is  worth  regarding  the  proper  correction  has  been  applied, 
using  for  the  purpose  the  mean  epochs  of  the  Twelve-year  catalogue,  which  are  only 
given  to  the  nearest  year.  For  reduction  to  apparent  place  the  special  catalogues  de- 
pend upon  the  Nautical  Almanac.  The  following  mean  corrections  for  nutation  and 
epoch  have  been  applied  : — 

Gh  39.     +  ".04  sin  (a  +  305°) 
Gh  45.     —  ".02  sin  (a  +    61°) 

Gh  50.  The  nutation  correction  is  : — 

-  ".05  sin  (a  +  76°) 

The  remarks  under  the  preceding  catalogues  are  generally  applicable.  A  portion 
of  the  time  the  mural  circle  was  used  in  a  temporary  observing-room,  and  the  circum- 
stances under  which  much  of  the  work  was  done  were  necessarily  unfavorable.  Some 
uncertainty  in  the  systematic  correction  of  this  catalogue  must  arise  from  the  fact  that 
it  combines  results  from  two  distinct  instruments  at  different  times. 

Gh  57.  This  catalogue  may  be  regarded  as  containing  the  work  of  the  transit  circle 
in  its  best  estate,  when  the  observers  had  become  accustomed  to  its  peculiarities,  and 
before  any  appreciable  imperfection  or  wear  had  resulted  from  long  use.  Though  the 
instrument  was  used  in  a  single  position  during  the  entire  period,  the  circle  readings 
were  made  with  six  microscopes.  Furthermore,  the  error  of  division  was  carefully 
examined  for  every  degree  and  for  some  special  divisions,  and  the  high  reputation  of 
the  makers  is  a  guarantee  that  the  accidental  errors  of  division  are  probably  small. 
The  proper  motions  of  this  and  succeeding  catalogues  of  Greenwich  are  generally  in 
fair  agreement  with  the  assumed  proper  motions,  so  that  this  correction  is  seldom 
applied  by  me.  The  special  catalogues,  until  1857,  require  small  corrections  for  nuta- 
tion and  epoch;  after  that  year  the  observations  were  reduced  with  Peters's  nutation, 
and  to  epoch  0  =  280°.  The  resulting  small  correction  was  neglected. 

Gh  64.  The  series  embraced  in  this  catalogue  is  essentially  a  continuation  of  the 
preceding.  No  correction  is  needed  save  that  for  proper  motion,  which  is  usually  insig- 
nificant. During  the  long  period  of  its  use  the  instrument  underwent  slow  changes 
from  wear,  which  might  be  quite  sufficient  to  cause  a  real  difference  in  the  systematic 
correction  required  (see  Gh  70). 

Gh  70.  The  slight  corrections  required  by  the  annual  variations  of  the  special  cat- 
alogues were  sometimes  regarded.  The  results  of  separate  years  were  then  combined 
with  weights  according  to  number  of  observations  in  each  year.  I  became  aware  of  the 


[35]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  441 

large  error  due  to  wear  of  the  micrometer  screws  too  late  to  make  any  use  of  a  special 
correction  on  that  account.  I  have  taken  my  information  from  Mr.  Christie's  paper 
in  Month.  Not.  R.  A.  S.,  for  November,  187G. 

The  series  of  reflection  observations  made  during  the  period  183G-1872,  at  Green- 
wich, has  attracted  wide  attention,  and  has  been  the  subject  of  some  interesting 
memoirs.  A  brief  consideration  of  the  principal  points  involved  will  be  of  use  in 
judging  the  value  of  the  declinations  in  the  absolute  sense.  During  most  of  the  period 

occupied  by  observations  with  the  mural  circles,  the  correction  — ^ —  was  found  to  be 

Jt 

so  small  and  so  irregular  that  it  could  not  safely  be  applied.*  The  corrections  of  earlier 
years,  and  for  1850,  were  small.  It  may,  therefore,  be  assumed  that  the  declinations 
of  that  period  (183G-1850)  are  practically  uninfluenced  by  the  discordance  in  question. 
On  the  introduction  of  the  great  transit  circle  in  1851  this  discordance  was  at  once 
noticeable,  and  a  correction  has  always  been  applied  to  all  polar  distances  deduced 
from  the  observations  of  this  instrument — this  correction  being  assumed  to  be  equal 
for  the  two  classes  of  observations  (direct  and  reflected),  but  applied  with  opposite 
signs.  The  division  error  was  discussed  for  every  degree  of  pointer  reading,  first  in 
1851-'2,  again  in  1856,  and  lastly  in  1871.  The  results  of  the  three  investigations 
essentially  confirm  each  other.  The  first  table  of  corrections  was  used  in  the  years 
1851-1856 ;  the  second,  1857-1867;  the  third,  which  is  the  mean  of  the  first  and  second, 
1868  and  later.  The  horizontal  flexure  was  several  times  determined  by  the  opposing 
horizontal  colliraators.  Until  1866  the  telescope  was  raised  from 'its  bearings  in  order 
to  render  the  collimators  intervisible.  In  the  latter  part  of  1865  the  telescope  cube 
was  pierced  in  such  a  manner  as  to  dispense  with  the  raising.  Owing  to  construction 
of  the  instrument  a  single  circular  opening  could  not  be  cut,  but  several  radiating 
apertures  in  the  form  of  sectors  were  made.  This  necessitated  the  use  of  .very  large 
collimators  (aperture  7  inches).  The  value  of  the  horizontal  flexure  suddenly  changed 
at  this  time  nearly  one  second,  passing  from  a  decided  plus  value  to  a  minus  value.  In 
the  table  to  be  given  it  will  be  observed  that  there  is  a  simultaneous  change  in  the 
opposite  direction  of  the  sign  of  the  coefficient  of  sin  Zcos?  Z.  As  Professor  Newcomb 
suggested  to  me  recently  that  the  entire  series  of  observations  with  the  transit  circle 
could  be  reconciled  to  the  supposition  of  a  uniform  coefficient  of  flexure,  depending 
on  sin  Z,  I  have  examined  this  question,  not,  however,  in  any  very  critical  or  conclu- 
sive manner.  It  is  necessary  to  remark  that  the  formula  of  correction  was,  until  1862, 

assumed  to  be 

(1)      a  +  b  sin  Z; 
subsequently  to  that  time 

(2)     a  +  b'  sin  Z  cos2  Z. 

I  have  reduced  b'  to  make  it  comparable  with  6,  by  supposing  that  the  mean  Z, 
where  D  —  R  occurs,  is  effectively  about  25°,  and,  therefore,  that  b  would  have  been 
about  .8  b',  had  the  law  expressed  in  (1)  been  used  instead  of  (2).  The  groups  are 
partly  determined  by  the  periods  during  which  the  same  coefficient  determined  from 
opposing  collimators  was  used.  The  following  table  exhibits  approximate  results. 
The  first  column  gives  the  year  or  period  ;  the  second,  adopted  value  of  flexure  depend- 

*Airy  says,  p.  xli,  Int.  Gh.  Obs.,  1840,  "  The  values  of  E  —  D  are  so  small,  and  the  existence  of  any 
law  among  them  so  uncertain,  that  I  have  thought  it  best  to  adopt  the  circle-results  without  any  correc- 
tion for  B  —  D."  This  remark  is  substantially  repeated  in  each  volume  until  1850. 


442 


UNITED  STATES  NORTHERN   BOUNDARY  COMMISSION. 


[30] 


ing  on  sin  Z,  obtained  from  observation  of  collimators ;  the  third,  the  average  value 
of  &  for  the  given  period — for  the  first  three  groups  directly  derived — for  all  after 
1862  from  V  in  the  manner  explained  ;  the  fourth,  the  average  value  of  the  constant 
term  a;  the  fifth,  the  sum  of  second  and  third  columns;  the  sixth,  the  weight — the 
result  of  one  year  being  the  unit.  The  spaces  indicate  epochs  of  change  in  division 
correction  used : — 


Period. 

Colliruator 
flexure. 

6,  or.  8&' 

(t 

Residual 
flexure. 

Weight. 

// 

II 

II 

a 

1851 
1852 
1853-1856 

+  .73 
+  .73 

+  .50 

—  .24 
[-  .24] 
—  .31 

+  .10 

[±:o°3] 

+  .49 
+  .19 

1 

4 

1857-1861 
1862-1864 
1865 
1866-1870* 

+  .56 
+  .56 
+  .76 
—  .37 

—  .42 
—  .43 
—  .62 
+  .62 

+  .04 
+  .01 
—  .04 
+  .10 

+  .14 
+  .13 
+  .14 
+  .25 

5 

3 
1 

5 

1871  and  1872 

—  .12 

+  .51 

—  .01 

+  .39 

2 

+  .21 

21 

*  The  actual  change  in  division  correction  used  took  place  in  1868,  and  is  unimportant. 

Thus  it  appears  that,  if  the  uniform  value  of  sine  flexure,  +  ".21,  had  been  employed 
throughout  ths  series,  we  should  have  had  sufficiently  good  agreement  between  direct 
and  reflection  observations.  This  appears  to  me  to  throw  discredit  upon  the  value  of 
flexure  derived  from  opposing  collimators,  and  forces  me  to  the  belief  that  the  change 
in  the  collimator  flexure  between  1865  and  1866,  if  it  has  indeed  any  reality  in  fact, 
was  much -smaller  than  has  been  supposed.  In  this  particular  case,  at  least,  the  fore- 
going discussion  appears  to  argue  strongly  for  the  utility  of  reflection  observations. 

.  If  there  is  a  real  residual  discordance,  E  —  D,  it  would  appear  from  the  discus- 
sions of  Airy  (Mem.  R.  A.  S.  xxxiii,  and  Seven-year  Catalogue,  p.  viii);  Faye  (Comptes 
.Eewrfws,  xxi,  pp.  401,  635,  757);  and  Van  de  Sande  Backhuyzen*  (Ast.  Nach.  1720), 
that  it  is  probably  due  in  some  measure  to  the  effect  of  variations  of  temperature  at 
different  altitudes  in  the  observing  room.  It  is  quite  likely,  that  the  reflection  obser- 
vations are  principally  affected — as  Henderson  and  others  have  supposed. 

It  may  be  interesting  to  note  that,  if  we  assume  the  latitude  derived  by  Bessel 
from  Bradley's  observations  (Fund.  Astr.)  to  be  near  the  truth — and  there  is  good 
reason  for  believing  it  is — and  if  we  suppose  the  mean  latitude  for  the  period  1836- 


1860  to  be  that  which  is  affected  by  the  correction 


R-D 


we  shall  have : — 


1755  :  <p  =  510  28'  39".6 
1847  :  ?  =  51°  28'  3S".17, 


*  "  Ueber  den  Einfluss  dcr  Strahlenbrechung  im  JBeobachtungesaale,  auf  die  mit  dem  Meridiankreise  besttm- 
ten  Declinationen."  This  paper  treats,  most  thoroughly,  the  observations  of  Greenwich  transit  circle, 
1851-1864,  with  reference  to  discrepancies  in  polar  distance,  which  are  cotemporaneous  with  difference 
of  readings  of  outer  and  inner  thermometers.  As  a  practical  result,  the  form  of  an  ideal  surface  of  junc- 
tion between  the  outer  and  inner  air  is  deduced,  which  appears  to  explain  the  discrepancies  in  a  satis- 
factory manner. 


[37J 


EBPORT  OF  THE  CHIEF  ASTEONOMEB,  APPENDIX  H.  443 


Annual  variation  of  latitude  —".0155,  or  —".0139,  if  the  latitudes  are  reduced  to 
the  same  refractions. 

Comparing  the  results  found  by  Airy  (p.  viii,  Seven-year  Catalogue),  with 
V  =  51°  28'  38".  17  -  ".0139 1,  we  have  :— 


Period. 

Latitude  observed. 

From  formula. 

o      /          // 

o        /         // 

1836-1841 

1842-1848 
1851-1860 

51    28    38.23 
38.17 
38.15 

51    28    38.28 
38.19 
38.04 

If,  on  the  other  hand,  we  consider  the  results  for  latitude  as  printed  in  the  Green- 
wich Annual  Catalogues  later  than  1860,  we  have  seconds  of  latitude  for  1861-07, 
38".25 ;  and  (after  approximate  reduction  to  the  refractions  previously  used)  for  1868- 
72,  38".18,  results  which  contradict  the  theory  of  diminishing  latitudes. 

EADCLIFFE    CATALOGUES. 

Ee  45.  The  nutation  correction  is  neglected,  because  the  period  embraced  in  the 
observations  is  so  great,  that  an  error  greater  than  the  correction  would  often  be  intro- 
duced. The  places  were  corrected,  wherever  necessary,  for  the  difference  between 
assumed  proper  motion  and  that  found  in  the  catalogue.  An  important  correction  is 
found  in  the  Introduction,  pp.  viii  to  xi.  This  has  been  carefully  applied,  as  well  as 
that  for  error  in  reducing  three  stars  specified,  p.  xii,  Int. 

The  refractions  used  in  this  catalogue  are  those  of  Bessel  (1820)  multiplied  by 
.9967.  A  much  smaller  refraction  was  deduced  by  Johnson  (Ee  Obs.  xv,  p.  xxiv).  The 
instrument  was  very  imperfect,  and  was  used  in  a  single  position. 

Ee  58.  This  is  essentially  a  continuation  of  the  foregoing  catalogue.  The  impor- 
tant correction  p.  xviii  Introduction  to  second  Radcliffo  catalogue  was  applied  before 
using  the  results. 

Ee  66  and  Ee  72.  The  trifling  correction  for  proper  motion  has  been  applied  in  a 
few  instances.  The  telescope  was  shifted  relatively  to  the  circle  at  the  beginning  of 
1870 ;  so  that  in  the  final  discussion  of  declinations  the  series  has  been  divided  into 
two  groups.  In  making  up  these  groups  the  observations  were  given  weights  propor- 
tional to  number  of  observations,  the  corrections  of  Table  IX.  being  first  applied. 
The  results  were  then  considered  as  agreeing  with  the  Normal  System  and  were  used 
without  further  correction.  But,  for  preliminary  purposes,  owing  to  the  large  system- 
atic differences  in  polar  distances  of  different  years,  stars  were  omitted  which  were  not 
observed  in  at  least  four  different  years.  Each  year  was  given  equal  weight  unless 
the  number  of  observations  was  less  than  4;  two  or  three  observations  were  given 
weight  .7;  and  1,  weight  .4.  The  following  table  exhibits  corrections  to  assumed  places 
thus  derived : — 


Star. 

c. 

Star. 

c. 

Star. 

C. 

It 

26 

It 

—     14 

51  Andromeda^  .  

—  .59 

-f-     39 

—    12 

o     Pise  in  in      .  

—  .78 

a    Cassiopecs  

—  .04 

a    Ursse  Minoris  

—  .26 

e    CassiopesB  

+  .20 

+    08 

O1   Ceti 

4-    (i4 

/?    Arietis    .  

—  .12 

-i_     28 

—  .00 

00  CiissiopciB  .  ... 

•4-  .57 

444 


UNITED  STATES  NORTHERN   BOUNDARY  COMMISSION. 


[38J 


Star. 

0 

Star. 

C 

Star. 

C 

a 

+  .15 
—  .17 
+  .25 
—  .09 
+  .31 

+1.23 
—  .23 

+  .71 
+  -.C1 
-  .28 

+  .06 
—  .01 
+  .12 
+  .29 
+  .29 

+  .22 
+  .13 
—  .07 

—  .87 
+  .55 

—  .24 
+1.23 
+  .01 
+  .02 
+  -11 
+  .93 
+  .06 
+  .49 
—  .54 
+  -21 

+  -14 
—  .25 

+1.32 
+  .09 
—  .10 

+  .21 
+  .27 
+  .19 

+  .08 
+  .57 

—  .54 
+  .OS 
62 

K    Draconis  

// 

+1.08 
+  .21 
—  .40 
+  .26 
—  .43 

—1.  02 
.12 

0    Cephei  

a 

+  .04 
+  .74 
—  .24 
—1.74 

+1.48 

—  .04 

f1   Ceti 

a    Can.  Ven  

a    Dolpbini  .    

g2   ceti 

6     Virginia...  .  

a    Cvgjni  

y3   Ceti 

a    Virginia  .  

//    Aquarii  . 

f  '    Ursaj  Majoris  

Gl'Cvorni.- 

ft    Persei 

C    Virginia  

C    Cvtrni  .. 

TJ    Ursa}  Majoris  . 

a    Cepbei  

+  .10 
+  .06 
-  .09 
—1.04 

+  .11 
+  .21 
+  .04 
—  .62 

+  .59 

—  .15 
—  .33 
+  .65 
+  .43 
+  .10 

—1.27 
+  .21 
+1.57 
+  .02 
+  .16 

—  .62 

—  .08 
—  .11 
+  .19 
+  .39 
-  .07 

—  .68 
+  .34 
+  .06 
+1.40 
+  .96 

—  .48 
+  .02 
—3.26 
+  .03 

—  .77 

rt    Bootis  

—  .03 
+  .03 
—  .55 

—  .08 
+  .39 
+  .46 
+  .17 

—  .80 

+  .37 
—  .79 

—  .80 
—  .20 
+  .44 

+  .48 
—  .31 
+  .27 
—  .04 

+  .68 

—  .45 
+  .03 
—1.07 
+  .07 
—1.53 

+  1.11 
+  .76 
—  .38 
+1.10 
+  .13 

+  .26 
+  .51 
34 

p    Aquarii  

BAG  1235 

(3    Cephei  

a    Bootis  

e     Aquarii  

e     Tauri 

0    Bootis........ 

e    Pegasi  

p    Bootis  .     ..... 

16  Pegasi  

4    Cainelopardalis    .  . 

el    Bootis        

a    A<i  uuri  i  

{3    Ursaj  Minoris  . 

0    Aquarii  

/3    Bootis          

y    Aquarii  

<J2   Cephei  

/?    Tauri               . 

17    Aquarii  

t    Pccrasi  . 

o    Coronas  Borealis  -  . 

I*.    Pegasi  

t     Cephei  

s     Serpent:s..  .. 

A    Aquarii  .. 

a    Pegasi  

o    Cephei  .  ......  .... 

t     Piscium  

BAG  2157 

15  Draconis  ...  ..... 

Stars  south  of  —  10°. 
(3    Ceti  

(3    Can.Minoris  
(3    Gemioorum  
(3    Cancrj  

C     Opliiuchi  .  ..  .  

£    Herculis  ...  

71    Herculis  

K.    Ophiuchi  .  ..4.  ... 

t,     Hvdrae  . 

e     Herculis  

a2   U  raad  Majoris  
K     Cancri  

e     Ursai  Minoris  . 

a1   Hercnlis  

a    Hydra?      

0    Draconis  

a    Ophiuchi  .  ... 

y1  Eridani  

v     Ursae  Majoris    

a    Leporis  

89  Herculis..  . 

+  -47 
—  .02 

—  .03 
+  .74 
+  .03 
—  .07 
+  .50 

+  -78 
+  .58 
+  .98 
+  .20 
+  .62 

+  .52 
+  .27 
+  .33 
+  .74 
+  .63 

e     Can.  Majoris  

y    Draconis.  ... 

15  Argus  

6    Crateria  

/3    Corvi  

(3    Ursse  Majoris  
i/j    Ursae  Majoris  

69 

pl   Scorpii  

+  .31 

+  .16 
+  .04 
+1.28 
—  .05 
+  .37 

+  .16 
—  .21 
+  .11 
—  .54 
—  .51 

a    Scorpii  

44  Ophiuchi  

fil   Sagittarii  

43  Sagittarii  
a3  Capricorn!  

6     Cvani 

X    Ursas  Majoris  
3    Leonia  . 

a    Pie.  Aust  

/?    Virginia 

/?    Aquileo  ........... 

y    Ursa3  Majoris  
<J     Ureas  Majoris  
ij    Virginia  

\    Ursse  Minoris  
K    Cephei  ........... 

NOTE. — The  catalogue  for  1873  was  not  received  in  time  to  be  used  in  forming  the  above  corrections, 
but  is  used  later  in  making  up  C,,  for  Re  72. 


[391 


REPORT  OP  THE  CHIEF  ASTRONOMER,  APPENDIX  H.         445 


In  forming  the  corrections,  a  few  polar  distances  marked  in  the  catalogues  as 
doubtful,  or  to  be  rejected,  with  a  few  which  result  solely  from  observations  below  the 
pole  at  great  zenith  distances,  were  not  used.  The  weights  of  a  few  others  were 
reduced  in  forming  the  means,  on  account  of  unusual  discordance,  or  because  the  cat- 
alogue p.  d.  is  made  up  partly  of  sub  polo  determinations  at  zenith  distances  over  70°. 

In  general,  the  results  are  far  less  exact  than  we  should  have  expected  from  the 
circumstances.  Though  the  instrument  is  of  the  non-reversible  pattern,  the  relation 
of  the  telescope  to  the  divided  circle  can  be  altered  at  pleasure;  yet  this  precaution 
was  exercised  but  once,  at  the  beginning  of  1870.  It  would  bo  impossible  to  detail  the 
various  systematic  corrections  which  have  been  applied  in  the  reductions  from  time 
to  time.  The  division  error  was  determined  on  the  assumption  that  the  mean  of  8 
microscopes  is  free  from  error,  and  a  correction  applied  after  1862.  The  values  of 
horizontal  flexure  as  adopted  in  reductions  have  varied  from  + 1".13  to  +  2".82. 
The  dependence  on  the  time  is  not  marked,  the  adopted  value  in  1862-'G3  being 
+  2".5 ;  and  in  1871-'73,  +  2".8.  In  1862-'63-'64  and  '67,  corrections  were  applied 


for 


E-  D 

2     • 


Various  corrections  were  applied  for  discordance  of  zenith  points,  deter- 


mined by  nadirs  and  by  reflection  observations,  etc.  The  refractions  are  those  deduced 
by  Johnson,  and  used  in  the  Radcliffe  general  catalogues.  To  show  the  variety  of 
practice  in  reducing  the  observations,  we  have  the  following  table  of  latitudes  adopted 
in  reductions : — 


Year. 

Adopted  latitude. 

Year. 

Adopted  latitude. 

O           '              /' 

o        /          " 

1862 

51    45    35.85 

1869 

51    45    35.42 

1863 

35.  73 

1864 

35.  50 

1370 

36.20 

1865 

35.28 

1871 

35.  81 

1866 

36.55 

1872 

36.06 

1867 

35.96 

1873 

36.33 

1868 

36.  16 

The  groups  indicate  periods  for  which  the  zenithal  circle  readings  were  the  same. 

Pa  45.  The  catalogue  results  are  used  without  change.  The  instrument  used  in 
these  observations  is  of  peculiar  construction,  and  in  many  respects  superior  to  any 
yet  employed  in  meridian  observations  for  the  purpose  of  deducing  standard  decli 
nations.  The  results  like  those  of  Kg  21,  Dt  24,  and  Ao  29  are  independent  in  every 
essential  respect,  and  are  such  as  to  inspire  the  highest  confidence. 

Ah  41  and  Ah  52.  It  was  decided  to  use  tbe  Armagh  places  for  1S40  as  two  cata- 
logues. The  first  includes  the  observations  1835-1846;  the  second,  1847-1854. 
Where  a  star  had  been  observed  in  both  periods,  the  separation  was  accomplished  in 
this  manner.  In  the  section  entitled  "Observed  Places  of  Stars,"  pp.  1  to  646,  the 
means,  for  each  period,  of  corrections  to  the  assumed  polar  distance  (that  of  A.  S.  C., 
B.  A.  0.,  etc.),  were  taken.  The  mean  of  all  the  results  was  then  subtracted  from  the 
separate  means;  the  results  are  corrections  to  the  catalogue  polar  distances  for  the 
respective  periods.  In  the  majority  of  instances  all  the  observations  of  a  given  star 
are  embraced  in  one  or  the  other  of  the  two  periods.  No  correction  for  nutation  was 


446         UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[40] 


applied.    Tbe  catalogue  places  are  reduced  without  proper  motion  except  in  a  few 
cases  specified  by  Dr.  Robinson  in  Ast.  Nach.  Ix,  75.    The  proper  correction  has  been 

carefully  applied. 

WASHINGTON  MURAL  CIRCLE,  1845-1873. 

The  most  of  this  series,  together  with  observations  of  meridian  circle,  meridian 
transit,  and  prime  vertical  transit,  have  been  compiled  in  a  general  catalogue*  for  the 
epoch  1860,  by  Professor  Yarnall.  For  the  present  purpose  it  is  desirable  to  separate 
the  work  of  the  various  instruments,  and  to  combine  the  work  of  the  inural  circle  into 
such  convenient  groups  as  appear  to  be  advisable.  The  error  of  division  of  this 
instrument  though  not  investigated  is  undoubtedly  small,  and  to  provide  against 
error  from  this  and  other  causes  the  position  of  the  telescope  on  the  circle  was  fre- 
quently changed. 

Wn  47.  The  declinations  are  reduc(d  in  1845  with  Lindenau's  nutation;  in  the 
three  following  years  with  that  of  the  B.  A.  0.,  and  to  epoch,  o  =  281°.  The  correc- 
tions are : — 

+  ".21  sin  (a  +  3150.2) 

+  ".05  sin  (a  +  244°  ) 
+  ".06  sin  (a  +  244°  ) 
+  ".06  sin  (a  +  247°  ) 

The  proper  motions  employed  in  the  reductions  are  those  of  N.  A.,  1848,  and 
B.  A.  C.  After  1845  the  declinations  are  reduced  to  1850.  so  that  the  correction  is 
often  considerable. 

The  latitude  which  results  from  the  observations  of  circumpolar  stars  in  1845,  and 
which  is  adopted  in  subsequent  years,  is  smaller  by  ".25  than  that  actually  employed 
in  the  reductions  of  1845.  Accordingly,  the  correction  —  ".25  has  been  applied  to  the 
catalogue  declinations  of  that  year,  reversing  the  sign  where  the  declination  results 
from  observations  below  the  pole. 

The  circle  was  used  in  thirty  different  positions,  relative  to  the  zenith,  in  1845 ; 
in  1846  and  1847  the  zenith  reading  remained  the  same,  and  was  again  changed  at 
the  beginning  of  1848.  The  process  of  combination  is  as  follows :  The  declinations 
of  1846  and  1847  are  combined  with  weights  proportional  to  the  number  of  observa- 
tions ;  to  the  resulting  declinations  for  1845,  1846-'47  and  1848  weights  are  assigned 
according  to  this  table : 


1845 
1846 
1847 
1848 


Weight. 

Number  ob- 
servations. 

Weight. 

Number  observa- 
tions. 

1 

1 

5 

8  to  11. 

2 

2 

6 

12  to  16. 

2.5 

3 

7 

17  to  26. 

3 

4 

8 

27  to  50. 

4 

5  to  7 

9    . 

51  and  upward. 

Wn  50.  The  simple  mean  of  the  separate  results  in  all  the  years  is  taken  without 
correction.    Professor  Hall  (Ast.  Nach.,  1947)  finds  the  correction  +  ".19  to  the  lati- 

*  'Catalogue  of  stars  observed  at  the  United  States  Naval  Observatory  during  the  years  1845  to 
1871."    Appendix  III.,  Washington  Astronomical  Observations  for  1871. 


[41] 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          447 


tuile  actually  used  in  reductions  (38°  53'  39".25).    The  resulting  correction  to  decli- 
ations,  I  have  not  used. 

Wn  04.  All  the  declinations  must  be  corrected  for  the  full  amount  of  proper 
•motion — that  of  a  Lyra  in  1862  excepted.  The  latitude  assumed  in  the  reductions 
should  be  corrected  by  —  ".47,  according  to  the  discussion  by  Professor  Newcoinb.* 
I  have  applied  to  all  declinations  above  the  pole  the  correction  —  ".47 ;  and  to  all 
below,  +  ".47.  To  all  the  declinations  by  direct  observations  in  1801  and  1802, 1  have 
applied  the  correction,  —  ".21  for  discordance  of  direct  and  reflected  observations,  on 
the  authority  -of  the  discussion,  p.  xxx,  Wash.  Ast.  Obs.  1803.  In  combination,  the 
weights  were  taken  from  the  table  given  in  Wash.  Obs.,  1804,  p.  xli,  which  is  here 
copied  for  reference : 


Weight. 

Number  of  observations  in  differ- 
ent years. 

1861-'62. 

1863. 

1864. 

1 

1  or  2  .... 
Above  2  .  . 

Ior2  .... 
3  to  5  .... 
Above  5.. 

1. 
2  or  3. 
4  to  7. 
8  to  20. 
Above  20. 

2 

3  

4  

5  

Wn  70.  All  declinations  are  corrected  tor  full  amount  of  proper  motion.  In  1872 
and  1873  the  assumed  latitude  is  38°  53'  38".8,  and  this  is  ".45  smaller  than  that  of 
previous  years.  +".45  is  applied  as  a  correction  to  the  catalogue  declinations  of 
1872-'73. 

So  51.  The  declinations  of  the  catalogue  are  used  without  alteration. 

So  55.  Proper  motions  were  employed  by  Mosta  in  a  few  cases  only.  These  are 
specified  on  p.  xli,  Int.  The  nutation  correction  is  that  of  Ce  55. 

Ps  53.  The  declinations  of  the  catalogue  are  used  without  change.  The  position 
of  the  telescope  on  the  circle  was  twice  changed  during  the  observations  of  this  series. 
There  is  every  reason  to  believe  that  the  observations  are  exceptionally  free  from  errors 
due  to  the  instrument  (Gambey  circle).  The  error  of  division  appears  to  have  been 
small  (vide  Lauiuer's  catalogue,  p.  55,  and  Compt.  Bend.,  tome,  xxvii,  p.  033). 

No  sensible  flexure  is  indicated  by  the  few  reflection  observations  which,  were  taken. 
Caillet's  refrac  ionst  were  adopted  in  the  reductions,  and  the  numerous  observations  of 
circumpolar  stars  do  not  indicate  any  considerable  correction  to  them. 

PAKIS  ANNUAL  CATALOGUES,  1854-'67. 

The  declinations  of  the  annual  catalogues  require  no  sensible  correction.  Until 
1802  the  Gambey  mural  circle  was  used  alone.  After  that  time  the  declinations  depend 
principally  upon  observations  made  with  the  great  meridian  circle.  The  position  of  the 
telescope  on  the  circle  was  changed  in  September,  1857.  A  comparison  between  results 
obtained  before  and  after  this  time  shows  that  there  is  a  constant  difference,  amounting, 
approximately,  to  ".25.  In  1863  and  1804  the  transit  circle  was  used  without  any  cor- 
rection for  flexure;  afterward  the  correction  —  ".77  sin  Z  was  applied  in  the  reductions. 

*  Appendix  to  Washington  Astronomical  Observations  for  1864. 
t  Additions  &  la  Conu.  des  temps,  1851. 


448         UNITED  STATES  NORTHERN    BOUNDARY  COMMISSION.  [42] 

Comparison  of  the  results  obtained  by  the  two  circles,  when  nsed  in  common, 
shows  no  appreciable  systematic  difference  between  them. 

The  declinations  are  not  independent — the  polar  points  being  derived  from  obser- 
vations of  the  stars  of  a  standard  catalogue,  the  places  of  which  are  revised  from  time 
to  time  on  the  authority  of  the  observations  themselves.  The  process  is  analogous  to 
that  commonly  adopted  in  the  determination  of  right  ascensions. 

The  separate  results  making  up  each  of  the  four  groups — 1854-'57,  1S5S-'G2,  1863- 
'64,  and  1865-'C7,  are  combined  with  weights  proportional  to  the  number  of  observa- 
tions. 

The  observed  declinations  of  stars,  not  included  in  the  Paris  standard  catalogue, 
are  not  conveniently  accessible,  and  the  apparent  places  for  the  days  of  observation 
only  are  given.  Consequently  they  have  been  used  only  in  a  few  special  cases. 

BRUSSELS  ANNUAL  CATALOGUES. 

The  declinations  of  these  catalogues  are  unaffected  by  the  reduction  for  proper 
motion,  except  for  stars  of  the  British  Nautical  Almanac.  I  have  applied  the  proper 
correction.  The  nutation  correction  for  1855  and  1856  is  identical  with  that  of  Cam- 
bridge for  corresponding  years. 

The  correction  for  division  was  not  applied  until  1857.  Though  there  is  no  appre- 
ciable alteration  in  methods  during  the  period  1857  to  1867,  the  observations  were 
divided  into  two  nearly  equal  groups — 1857-'62, 1863-'67 — by  which  means  greater 
accuracy  is  secured  in  the  solution  of  conditional  equations  according  to  the  adopted 
method.  This  is  the  more  to  be  desired  because  the  Brussels  series  contains  numerous 
observations  of  stars. generally  neglected,  elsewhere,  in  recent  times. 

The  combination  of  the  separate  years  in  each  of  tbe  three  groups  was  effected 
by  means  of  weights  strictly  proportional  to  the  number  of  observations. 

C  G  H  58.  The  proper  motions  employed  in  this  catalogue  are  usually  very  near 
those  assumed  in  this  paper.  Where  this  correction  becomes  sensible  it  has  been 
applied.  The  instrument  is  a  duplicate  of  the  Greenwich  transit  circle,  and  is  of  course 
subject  to  tbe  same  theoretical  objections.  Mr.  Stone  suspects  that  the  zenith  distances 
given  by  this  instrument  require  a  considerable  correction*,  which  is  proportional  to 
cos  Z.  This  will  tend  to  throw  suspicion  upon  the  results  of  the  discussion  of  refraction 
correction  in  introduction  to  the  Cape  catalogue  (p.  x).  This  discussion  indicates  that 
Bessel's  refractions  should  be  multiplied  by  .9953  in  order  to  correspond  to  the  obser- 
vations of  circumpolar  stars,  but  r.o  use  is  made  of  this  result  by  Mr.  Stone  in  forming 
the  catalogue. 

Me  62.  The  small  corrections  for  difference  between  assumed  and  catalogue  (Main's) 
proper  motions  have  been  applied,  also  the  table  of  corrections  for  flexure,  etc.,  given  in 
the  catalogue  (p.  xxi,  int.).  The  instrument  used  in  these,  and  subsequent  meridian 
observations  at  Melbourne,  is  similar  in  most  respects  to  the  Greeuwich  transit  circle. 
It  is  much  smaller,  however,  and  there  are  only  four  circle  microscopes. 

During  the  period  embraced  in  Me  62  the  instrument  was  used  at  Williamstown, 
a  short  distance  from  its  present  site.  The  instrumental  reductions  are  very  uncertain, 

•  Month.  Not.  R.  A.  S.,  vol.  33,  p.  69. 


[43J 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  U. 


449 


aud  the  circumstances  were  unfavorable  for  accurate  work.  The  declinations  are  prob- 
ably much  inferior  to  those  obtained  with  the  same  instrument  at  Melbourne. 

Me  68.  The  catalogue  polar  distances  are  reduced  to  1870,  with  proper  motions, 
which  seldom  differ  much  from  those  of  Section  II.  However,  the  resulting  small  cor- 
rections have  been  carefully  applied.  Following  the  discussion  by  Mr.  E.  J.  Stone 
(Month.  Not.,  vol.  38,  p.  27),  the  declinations  are  reduced  by  Mr.  Ellery  on  the  assump- 
tion that  for  stars  culminating  north  of  Melbourne  zenith,  Bessel's  refractions  should 
be  multiplied  by  .9909,  aud  for  stars  south  by  .9903.  The  latter  number  results  from 
observations  of  circumpolar  stars  at  Melbourne,  the  former  from  comparison  with  Green- 
wich declinations,  1857-'G5.  From  circumpolar  stars  Dr.  Gylden  has  found  .99718  (V. 
J.  S.  Bd.,  iv,  102),  and  arguments  derived  from  a  consideration  of  Cape  of  Good  Hope 
aud  St.  Helena  declinations,  compared  with  those  of  northern  observations,  incline  him 
to  the  belief  that  there  may  be  a  real  difference  in  the  refractions  for  the  two  sides  of 
the  zenith  at  Melbourne,  though  the  question  is  much  obscured  by  the  uncertainty  as 
to  division  error  and  flexure  of  the  instrument.  The  instrument  being  non-reversible 
we  must  remain  in  ignorance  as  to  the  amount  of  cosine  flexure,  and  while  this  uncer- 
tainty remains  it  will  be  difficult  to  draw  decided  conclusions  about  refraction,  espe- 
cially when  we  consider  the  necessarily  large  probable  error  of  refraction  determina- 
tions at  the  latitude  of  Melbourne.  The  comparison  of  Washington  and  Melbourne 
(p.  CO)  throws  some  further  light  on  the  matter. 

Bn  06.  The  declinations  taken  from  Ast.  NacJi.,  1719,  are  used  without  change;  those 
from  the  sixth  volume  of  Bonn  observations  are  corrected  for  the  full  amount  of  proper 
motion,  and  for  the  quantities  (applicable  to  declinations,  clamp  east)  in  the  following 
table,  which  is  extracted  from  the  introduction  to  the  volume  in  question  (p.  xiv): — 


<5 

Correction. 

<5 

Correction. 

o 

// 

c 

a 

—  25 

—  .51 

35 

+    47 

—  15 

—  .47 

45 

+    52 

—    5 

—  .38 

55 

+    50 

+    5 

—  .20 

65 

+    43 

+  15 

+  .06 

75 

4-    32 

+  25 

+  .:tt 

85 

+     13 

When  the  clamp  is  west  the  sign  of  the  correction  must  be  reversed.  The  decli- 
nations depend  essentially  upon  those  of  the  Berlin  Jahrbuch  (Wolfer's). 

Lc  CO.  The  declinations  must  be  corrected  for  the  full  amount  of  proper  motion, 
none  having  been  employed  in  the  reductions.  The  declinations  are  founded  syste- 
matically upon  the  standard  catalogue  of  the  German  Astronomical  Society  (V.  J.  8., 
iv,  324). 

Ln  07.  A  few  small  corrections  for  proper  motion  have  been  applied.  In  trans- 
cribing the  declinations  from  this  series,  the  order  of  preference  has  been — first,  Ast. 
Nach.,  1902;  second,  circumpolar  stars,  p.  [141],  second  volume  Leiden  Obs.;  third, 
from  the  catalogue  of  Gradmessung  stars,  p.  [12D]  ibid. 

The  stars  of  the  Gradmessung  catalogue  depend  upon  readings  of  circle  B  alone;  for 
the  others  both  circles  were  used.  Exceptional  care  appears  to  have  been  exercised  both 
N  B 29 


450          UNITED  STATES  NORTHERN    BOUNDARY  COMMISSION.  [44] 

in  the  observations  and  their  reductions.  The  instrument  is  of  the  reversible  pattern, 
and,  where  practicable,  equal  numbers  of  observations  have  been  taken  in  each  of  the 
four  positions— clamp  east  (dir.  aud  ref.),  clarap  west  (dir.  and  ref.).  The  error  of  division 
for  every  5'  mark  on  both  circles  has  been  ascertained.  The  corrections  for  flexure,  aud 
to  assumed  latitude  and  refraction  constant,  are  thoroughly  discussed  according  to  the 
methods  of  Bessel.  The  Gradmessung  stars  were  each  observed  -.ixteen  times — the 
others  much  more  frequently. 

RESULTS  OF  OBSERVATIONS  FOR  DECLINATION  HADE  WITH  THE  WASHINGTON  TRANSIT 

CIRCLE  FOR  YEARS  18GG-1874. 

These  are  printed  in  the  annual  volumes  of  the  United  States  Naval  Observatory 
for  the  respective  years,  and  have  been  taken  from  the  sections  entitled  "Corrections 
to  the  star  positions  of  the  American  Ephemeris/'etc.,  and  "Positions  of  Miscellaneous 
Stars,"  etc.  I  have  not  used  the  results  obtained  by  Professor  Newcomb,  from  tlio 
observations  of  I860  aud  1867,  aud  published  in  Appendix  III.  of  the  Washington 
volume  for  18G7,  nor  the  annual  catalogues  in  the  later  volumes. 

Notwithstanding  the  large  probable  error  of  its  single  determinations,  this  series 
appears  to  be  worthy  of  particular  attention,  both  on  account  of  the  great  variety  of 
circumstances  under  which  the  observations  were  taken,  and  because  the  instrument 
under  consideration  is  in  latitude  nearly  13°  farther  south  than  any  other  in  the 
northern  hemisphere  which  has  been  used  for  important  independent  determinations 
of  declination  in  recent  times. 

The  instrument,  one  of  the  largest  of  its  class,  is  easily  reversed.  It  has  two 
flnely  divided  circles,  denominated  respectively  A  and  B.  Circle  A  was  read  in  1866  and 
B  in  subsequent  years.  In  the  Washington  volume  for  1865  will  be  found  an  elaborate 
aud  exhaustive  treatise  by  Professor  oSTewcomb  relating  to  the  theory  of  errors  of  the 
transit  circle,  aud  iu  the  same  connection  a  practical  application  of  the  principles 
derived,  to  the  particular  case  of  the  Washington  transit  circle.  The  division  correc- 
tion of  each  circle  is  ascertained  with  great  care  at  intervals  of  single  degrees ;  the 
corrections  for  flexure  of  circles  aud  telescope  are  examined,  so  far  as  the  same  was 
practicable  without  recourse  to  celestial  observation.  The  reductions  of  subsequent 
years  assume  the  accuracy  of  these  investigations.  The  instrument  is  usually  reversed 
at  the  beginning  of  each  calendar  year,  aud  at  various  times  the  circle  is  shifted  rela- 
tively to  the  telescope,  so  that  a  given  polar  distance  will  depend  upon  different 
divisions  in  different  years.  The  only  exception  is  in  the  years  1871  and  1872,  which, 
for  practical  purposes,  may  be  regarded  as  the  work  of  a  single  year.  The  zenith 
points  until  June,  1867,  were  mainly  derived  from  observations  of  leveled  collimators; 
after  that  period  from  observations  of  the  nadir.  A  few  observations  by  reflection 
were  taken,  but  alter  the  first  three  years  the  number  of  these  is  so  scanty  that  no 
reliable  discussion  of  instrumental  peculiarities  can  be  based  upon  their  testimony. 
Besides  the  corrections  for  division  and  flexure  in  each  year,  certain  corrections  derived 
from  the  observations  for  polar  distance  are  applied  for  discordance  of  direct  aud 
reflected  observations  and  for  error  of  assumed  latitude,  so  that,  iu  effect,  the  results 
of  separate  years  are  essentially  independent  and  in  a  certain  sense  absolute. 

Perhaps  the  most  remarkable  feature  iu  the  method  of  reduction  pursued  through- 
out this  series  is  the  assumption  of  a  comparatively  sudden  change  near  the  zenith 


[45]  KEPOBT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  451 

iu  the  correction  for  discordance  of  direct  and  reflected  observations.    This  correction 
is  assumed  to  be  constant  from  90°  to  5°  northern  zenith  distance,  and  from  5°  to  90° 
southern  zenith  distance,  different  values  of  the  correction  being  applied  according  as 
tbe  object  observed  is  north  or  south.    Between  the  point  5°  north  and  that  which  is 
5°  south  the  value  of  the  correction  is  interpolated.    If  we  denote  by — 
AZ  the  corrections  actually  applied  to  polar  distances  between  5°  and  90°  zenith  dis- 
tance south, 
AZ1  the  corresponding  correction  for  polar  distances  between  the  limits  5°  and  90° 

zenith  distance  north, 
we  have  for  separate  years  the  following  values  of  AZ—AZ1. 


I860  -  ".47 

1867  —  ".60 

1868  -  ".68 

1869  -  ".18 


1870  +  ".31 
1871-2     [".OOJ 

1873  -  ".42 

1874  -  ".82 


The  difference  for  1871-2  was  actually  found  to  be  — 1".45,  but  its  improbable 
magnitude  led  to  its  rejection.  Consideration  of  the  values  of  latitude  derived  from 
the  observations  of  separate  years,  as  well  from  reflected  as  direct  observations,* 
strengthens  the  belief  that  too  much  reliance  has  been  placed  upon  the  results  of  the 
former.  In  view  of  the  precautions  which  were  taken,  the  adoption  of  a  sudden  varia- 
tion in  the  correction  applicable  to  polar  distances  near  the  zenith  is  at  least  open  to 
grave  objections,  while  the  persistence  in  the  sign  of  AZ—AZ1  during  the  entire  history 
of  the  circle  thus  far,  renders  it  highly  probable  that  the  discordance  iu  question  has 
been  produced  mainly  by  causes  which  are  independent  of  the  instrument  itself,  and 
which  affect,  perhaps  chiefly,  if  not  entirely,  observations  by  reflection.  Moreover,  the 
final  results  of  separate  years,  as  printed,  exhibit  considerable  systematic  discordances. 
I  therefore  resolved  to  investigate  the  relative  accuracy  of  the  results  for  separate 
years,  and,  with  certain  preliminary  assumptions,  to  derive  if  possible  from  the  obser- 
vations themselves  systematic  corrections,  which  should  appear  theoretically  admis- 
sible, and  which  might  at  the  same  time  produce  a  tolerable  degree  of  harmony.  It 
appeared  to  me  that  this  would  be  practicable  only  in  the  case  of  the  earlier  years, 
there  being  after  1868  few  observations  of  stars  at  lower  transit  or  by  reflection. 

In  1869  the  instrument  was  dismounted  and  placed  in  a  new  room  especially 
designed  for  its  use.  In  1870  the  object-glass  was  reground  and  other  important 
changes  accomplished.  These  and  other  considerations  have  led  to  a  division  of  the 
entire  series  into  two  distinct  portions,  viz  : 

Wn  68,  embracing  the  years  1866-1869. 
Wn  72,  years  1870-1874. 
Wn  68. 
The  following  notation  is  adopted  : 

Z=i  Zenith  distance,  reckoned  from  0°  to  360°  in  usual  direction. 
AZ=  Required  constant  correction  for  a  given  year  to  direct  zenith  distances,  as 

adopted  and  corrected  fur  division  error. 
D  =  Correction  for  division  error,  taken  from  tables  §  72  of  description  of  transit 

circle,  Wn.  Ast.  Obs.,  1865. 
*  See  p.  Ixxviii,  Introduction  to  Washington  Astronomical  Observa'ions  for  1873. 


452          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.  [46] 

P'  =  Polar  distauce  of  American  Ephemeris.    For  direct  observations  counted 

from  00  to  360°. 

Ap  =  Correction  given  to  P'  by  a  single  observation  of  polar  distance  as  printed 
in  the  column  entitled  "Miscellaneous  Corrections,"  in  the  sections  enti- 
tled "Observations  with  the  Transit  Circle;"  but  this  designation  is  also 
applied  to  the  same  quantity  when  corrected  for  errata  and  certain  cor- 
rections required  by  some  of  the  zenith  points  of  18G7  and  1868. 
AP,=  Mean  of  n  values  of  Ap.    Does  not  include  division  correction. 
AP=  AP,+  D. 

P  and  P,  for  stars  not  in  Am.  Eph,  correspond  to  P1  +  A  P  and  P  +  A  Pr 
F  =  Horizontal,  or  sine  flexure. 
f  ==  Zenithal,  or  cosine  flexure. 

A  <?  =  Correction  to  assumed  latitude,  —  38°  53'  38".80. 
P  and  p'  =  Computed  refractions,  respectively  for  the  upper  and  lower  culminations  of 

a  given  star. 
(1  —  lc)  =  Factor  by  which  these  must  be  multiplied  to  bring  them  in  accordance 

with  observation  of  circumpolar  stars. 
The  true  probable  error  of  any  final  result  for  a  given  star  in  a  single 

position  of  the  circle,  is  supposed  to  be  of  the  usual  formA/e/' 
where — 

e  =  Probable  error  of  a  single  pointing,  or  that  part  of  the  error  which  dimin- 
ishes according  to  the  value  of  -T=;  and 

e,  =  Probable  error  for  a  single  position  of  the  instrument  when  n  is  infinite. 
e  is  supposed  to  increase  with  the  zenith  distance  according  to  the  law 
£2  =  e,,2  +  £///2  tan2  Z;  where 
e//  =  value  of  £  when  Z  =  0 ;  and — 
e7//  =  arbitrary  constant. 
n'  =  Weight,  the  probable  error  of  whose  unit  is  E. 

Whenever  it  is  necessary  to  limit  the  application  of  the  above  quantities 
to  a  particular  year  or  mode  of  observation  it  is  effected  by  adding  to  the 
expression  for  the  quantity  the  designations  66,  67,  68,  69,  or  (Dir),  (Ret), 
etc.  These  designations  are  omitted  in  many  cases  where  no  ambiguity 
can  arise  from  that  course. 

The  change  in  method  of  obtaining  zenith  point,  which  took  place  in  18G7, 
requires  an  examination  of  the  determinations  of  north  polar  distance  in  that  year,  for 
the  purpose  of  ascertaining  whether  there  is  any  constant  difference  between  the 
results  obtained  before  and  after  June  1,  when  the  change  took  place.  To  settle  this 
point,  the  direct  observations  of  70  stars  most  frequently  observed  (and  at  least  three 
times  in  each  period)  were  selected.  The  observations  previous  to  June  1  were 
grouped  in  a  single  mean,  A  P, ;  and  those  subsequent,  in  another,  A  Pir  Weights 
were  assigned  according  to  the  usual  formula :  i.  e.,  n,  being  the  number  of  observa- 
tions making  up  A  P,  and  n,,  the  number  of  observations  making  up  A  P,,,  we  have 

JT  =    n'  n"  .    These  weights  were  taken  roughly  to  the  nearest  unit.    The  resulting 


[47] 


EBPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


453 


value  of  the  correction  is 

AP,-APII  =  -  ".34  i  ".032 ;  weight  294. 
e67  =  ±  ".55. 

All  the  polar  distances  subsequent  to  June  1  were  consequently  corrected  by  —  ".34, 
to  bring  them  into  systematic  accordance  with  those  values  of  Ap  obtained  previous 
to  that  date.  Where  the  number  of  determinations  for  a  given  star  is  small,  particular 
examination  of  observations  made  in  May  was  instituted,  and  such  observations  in 
that  month  as  appeared  to  depend  on  Nadirs  were  corrected.  AP&  was  then  formed 
anew,  respect  being  had  for  the  list  of  errata  (end  of  this  Appendix). 

Even  a  superficial  examination  of  the  results  for  1868  is  sufficient  to  show  that 
the  probable  error,  eM.  is  much  larger  than  the  corresponding  quantity  for  any  other 
year,  and  while  it  was  found  to  be  impracticable  if  not  impossible  to  assign  all  the 
reasons  for  this,  an  examination  leaves  no  doubt  that  it  is  partly  due  to  constant  errors 
in  the  determination  of  zenith  paint  correction.  Some  of  these  errors  are  quite  large, 
and  though  extreme  caution  should  be  exercised,  I  have  not  hesitated  to  apply  the 
more  important  corrections  which  seemed  to  be  required.  I  have  followed  a  method 
precisely  like  that  adopted  by  Professor  Newcomb  in  similar  cases  occurring  in  1866.* 
The  suspected  periods  were  quite  numerous,  but  only  those  in  the  subjoined  table 
were  adopted  for  treatment.  A  Pn  for  each  star  common  to  any  one  or  more  of  these 
nights,  was  formed  from  all  the  remaining  observations  of  the  year ;  and  theu  each 
compared  with  the  questionable  values  of  its  corresponding  A  p.  Thus  a  series  of 
values  A  Pt  —  Ap  were  obtained  for  each  date,  and  the  mean  of  each  set  adopted  as 
the  correction  to  the  results  as  printed.  The  column  headed  "No."  shows  the  total 
number  of  values  of  A  P,  —  Ap,  which  are  used  to  form  the  corresponding  correction. 
The  corrections  with  reversed  signs  are  applicable  to  the  results  of  reflection  obser- 
vations. 


Date. 

Observer. 

Correction. 

No. 

Remarks. 

March  18... 

H 

a 
+  1.5 

10 

Polaris  to  K  Cancri. 

September  7 

F 

—  1.5 

19 

October  1  ... 

T 

—  2.0 

16 

October  13  .  . 

F 

—  3.0 

19 

October  16.. 

F 

—  1.7 

16 

November  6. 

E 

—  0.9 

22 

f  Cygni  to  Polaris. 

November  6. 

E 

—  2.3 

11 

i  Canis  Majoris  to  a  Hydra. 

Decembers. 

F 

—  1.2 

14* 

*  The  result  from  a  Aquilce  is  excluded. 

The  corrections  on  November  6,  taken  in  connection  with  the  corresponding 
"zenith  point  corrections,"  which  for  the  first  group  was  13".0,  and  for  the  second 
14",3,  show  that  the  Nadir  determinations  may  indicate  a  considerable  change  in  the 
zenith  point  without  any  real  alteration.  The  "zenith  point  corrections"  on  November 
6,  according  to  the  above  table,  should  have  been  12".l  and  12".0  respectively,  for  the 
first  and  second  groups ;  while  they  were  found  to  be  from  Nadir  observations  on 
*  Washington  Astronomical  Observations,  1866,  p.  xvii.  Introduction. 


454          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[48] 


November  5,  11".9,  on  November  7,  13".2,  and  on  November  9,  10".G,  each  depending 
on  two  separate  observations,  —  those  on  November  7  being  respectively  14".58  and 
11".97. 

The  only  remaining  corrections  adopted  to  aid  in  forming  A  P  in  this  and  in  other 
years  are  for  errata,  which  are  to  be  found  at  the  end  of  this  Appendix.  Twenty 
seven  observations  in  1868  which  differed  more  than  3".5  from  the  concluded  means, 
were  rejected. 

In  1866  the  values  of  A  P  resulting  from  zenith  points  as  corrected  are  adopted. 

Probable  Error. 

Before  combining  the  results  of  separate  years,  it  is  important  to  know  their  rela- 
tive weights  ;  especially  as  an  examination,  merely  preliminary,  shows  that  the  accu- 
racy of  a  single  determination  varies  greatly  in  different  years.  In  getting  probable 
error,  the  corrected  results  were  used  in  18G6  ;  and  the  results  as  printed  and  corrected 
for  errata,  in  subsequent  years  ;  except  that  the  rejected  observations  of  1868  were  not 
included.  Each  Ap  was  compared  with  its  A  P,  and  the  residuals  arranged  in  groups 
according  to  zenith  distance.  The  probable  error  E  was  supposed  to  follow  the  well- 
known  law* 


Whatever  the  theoretical  objections  to  this  formula,  they  are  nothing  in  com- 
parison with  the  uncertainty  of  the  determination;  because  in  this  particular  case 
there  are  few  observations  at  great  zenith  distances.  No  distinction  is  made  between 
observations  north  or  south  of  the  zenith,  owing  to  the  considerable  number  of  bisec- 
tions taken  at  each  pointing;  and  these,  for  northern  stars  frequently  observed,  are 
more  numerous  on  the  average  than  for  the  southern  ;  so  that  the  greater  accuracy  in 
a  single  bisection  of  an  equatorial  star  is  in  this  way  assumed  to  give  no  marked 
advantage.  In  1866  and  1867,  stars  observed  twenty  times  or  more  were  used,  except 
at  zenith  distances  greater  than  55°,  where  the  minimum  was  reduced  to  7  observa- 
tions of  the  same  star.  In  the  two  succeeding  years  the  minimum  for  zenith  distances 
less  than  60°  is  10.  The  results  follow:— 

1866. 


Group. 

Meau^ 

No.  resid- 
uals. 

Observed  s 

e  from 
formula. 

1 

2 

3 
4 

5 
6 

o 
6 
20 
28 
43 
51 
58 

210 
202 
194 
212 
251 
201 

: 

II 

-  .54 
-  .52 
-  .58 
'-  .63 

:  .71 
:  .65 

s  fefeSSSfe 
-H-H-H-H-H-H 

1867. 

1 
2 
3 
4 
5 
6 

10 
25 
49 
53 
59 
60 

226 
232 
205 
127 

85 
31 

±  .51 
±  .55 
±  .53 
±  .60 
±  .54 
±.74 

-  .51 
-  .52 

:  .55 

^  .57 

:  .59 
:  .71 

Vide  Langier's  Memoir ;  Kaiser,  Second  Volume  Leiden  Observations,  etc. 


[49] 


EBPOBT  OF  THE  CHIEF  ASTRONOMER.  APPENDIX  H. 


455 


1868. 


Group. 

Mean  Z 

No.  resirt- 
ual.-s. 

Observed  e 

F  from 
formula. 

o 

a 

// 

1 

8 

1119 

±  .86 

±  -76 

2 

21 

2^9 

±  -71 

t  .76 

3 

32 

395 

±  .76 

±  .77 

4 

50 

343 

±  -77 

±  .79 

5 

50 

79 

±  .72 

±  .81 

6 

65 

83 

±  .60 

±  -86 

7 

72 

45 

±1.00 

±  .96 

Two  bundred  and  eighty-seven  residuals  of  stars  most  frequently  observed  in  1869 
give  e  =  ±  .67. 

One  bundred  and  sixty-five  residuals  of  stars  most  frequently  observed  by  reflec- 
tion iu  1867  give  e  —  ±  ".50. 

The  following  formulae  were  adopted  for  the  respective  years  : 

1866 
1867 
1868 
1869 

For  1868  the  factor  multiplied  by  tangz#  was  assumed  equal  to  that  found  by 
experiment  in  1867  ;  the  result  for  1868  being  of  extremely  small  weight. 

For  1869  the  formula  found  from  the  observations  of  Wn  1870-1873  was  adopted 
as  being  a  close  approximation. 

With  the  arguments  Z  and  year,  we  have  the  following  table  of  — 

Valves  of  e 


=  ".323    +   ".0450 

=  ".261    +   ".0333 

=  ".578    +  (".0333)  tang2Z 

=  (".455)  +  (".0415) 


Z  — 

0° 

20° 

30° 

40° 

50° 

55° 

60° 

65° 

70° 

75° 

1866 

II 

.57 

II 

.57 

II 

.58 

II 

.60 

II 

.62 

it 
.64 

.68 

n 
.73 

II 

.81 

*/ 

.97 

1867" 

.51 

.52 

.52 

.53 

.55 

.57 

.60 

.64 

.72 

.85 

1868 

.76 

.76 

.77 

.78 

.79 

.80 

.82 

.86 

.91 

1.02 

1869 

.68 

.68 

.68 

.70 

.72 

.74 

.76 

.80 

.88 

1.02 

The  value  of  e,  must  be  determined  from  a  comparison  of  observations  in  different 
positions  of  the  circle. 

It  will  now  be  assumed  that  the  systematic  corrections  required  by  the  adopted 
values  of  A  P,  are :  a,  a  correction  D  for  division  error.  This  has  been  taken  from 
tables  in  §  72  of  the  description  of  the  transit  circle,  Washington  Observations  for 
1865. 

fe,  a  constant  correction,  —  A  Z,  to  all  of  the  zenith  points  of  a  given  year.  The 
correction  to  A  P  will  be  +  J  Z. 

*  The  value  of  eCT  at  50°Z  agrees  precisely  with  that  found  in  another  way  (see  p.  47).    The  value 
there  found  corresponds  to  a  zenith  distance  of  about  40°. 


456          UNITED  STATES  NOETBEKN  BOUNDARY  COMMISSION.  [50] 

c,  a  correction  for  flexure,  arbitrarily  assumed  to  be  of  the  form  F  sin  Z  +  F'  cos  Z. 

d,  a  correction,  —  J  <p  ,  to  A  P  (18G6-18G9)  for  error  in  the  assumed  latitude,  38°  53' 
38".80. 

These  corrections  are  of  the  forms  usually  adopted,  and  seem  to  require  no  ex- 
planation on  theoretical  grounds. 

Accepting  these,  the  final  polar  distance  by  direct  observation  will  be  — 


Of  these  corrections  /I  Z  will  vary  with  the  year;  A  <f>  will  be  constant;  and  J>,  F 
and  F'  will  depend  upon  the  reading  of  the  circle  used. 

Values  of  JZ,F  and  F1. 

During  the  years  1867  and  1868  circle  B  was  used.  It  was  reversed  at  the  begin- 
ning of  1868,  but  was  not  shifted  relatively  to  the  telescope.  In  each  year  there  is 
a  considerable  number  of  reflection  observations,  both  north  and  south.  The  neces- 
sary conditions  are  thus  established  for  ascertaining  the  quantities  JZ67,  dZG8,F 
and  F'.  F  and  F'  have  been  already  investigated  as  stated  above*  (p.  44)  ;  but  that 
portion  of  F'  which  depends  upon  the  flexure  of  the  telescope  could  only  be  roughly 
inferred,  and  was  taken  as  .00.  So  far  as  this  assumption  is  supported  by  the  present 
investigation,  it  will  be  found  to  be  substantially  correct.  However  the  discordance 
between  the  direct  and  reflected  observations  of  these  and  other  years  may  originate, 
if  one  of  the  possible  causes  of  error  is  known,  and  if  the  form  of  the  differences  can 
be  reconciled,  within  a  fair  degree  of  probability,  to  represent  the  effect  of  that  cause, 
we  are  bound  to  accept  the  latter,  provisionally,  as  the  most  probable,  or  at  least  as  an 
important  source  of  the  difficulty.  If  other  means  of  measuring  the  effect  of  the  known 
disturbing  agency  exist  and  have  been  employed,  the  question  then  relates  to  the  weight 
of  each  determination  or  method,  and,  except  for  considerations  of  expediency,  neither 
should  be  adopted  to  the  exclusion  of  others,  unless  there  is  great  disparity  of 
weights. 

It  is  a  priori  possible  that  the  whole  or  a  part  of  the  discordance  in  question  may 
be  produced  by  flexure.  The  horizontal  flexure  (F)  has  been  measured  by  opposing 
collimators  and  also  by  the  aid  of  leveled  collimators,  in  the  manner  detailed  in  the 
Washington  volume  for  1865-t  The  definitive  result  was  taken  from  the  former  method. 
The  values  given  by  leveled  collimators,  for  reasons  stated,  are  justly  regarded  as  of 
little  weight,  though  it  will  be  seen  that  their  mean  is  very  near  the  mean  finally 
adopted  in  this  discussion.  Professor  Newcomb  considers  the  flexure  of  the  circles  and 
of  the  telescope  separately.  The  former  was  ascertained  by  a  method  of  comparing 
simultaneous  readings  of  the  two  circles,  combined  with  a  systematic  rotation  in  their 
relative  positions.  The  flexure  of  the  telescope  in  the  horizontal  position  was  deter- 
mined by  subtracting  from  the  value  of  F,  found  by  opposing  collimators,  that  pre- 
viously found  for  the  circle  read  in  the  observation.  A  rough  check  on  the  zenithal 
flexure  of  telescope  was  obtained  in  an  analogous  manner  by  the  aid  of  nadir  observa- 
tions combined  with  readings  on  leveled  collimators.  The  result  is  confessedly  of  small 

"Washington  Astronomical  Observations  for  1866,  Appendix  I,  $  60  to  $  67. 
t  $  (65)  App.  I.,  Wn.  Obs.,  1865. 


[51] 


REPORT  OP  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          457 


weight.  Many  of  tbe  determinations  by  opposing  collimators  were  known  to  be  influ- 
enced by  temperature  in  the  room  varying  at  different  altitudes,  and  such  were  rejected. 
It  is  not  altogether  improbable  that  the  measures  accepted  may  have  been  affected 
injuriously  by  the  same  cause,  though  in  a  smaller  degree.  They  are  also  liable  to 
error  from  other  causes,  among  which  may  be  mentioned  personal  error,  and  the  error 
possibly  arising  from  the  small  aperture  of  the  collimators.*  It  would  be  difficult  to 
estimate  the  probable  error  in  the  determination  of  F  and  F' ;  but  perhaps  enough  has 
been  said  to  show  that  a  considerable  correction  to  the  adopted  values  is  not  altogether 
inadmissible. 

The  reflection-observations  of  1867  and  1868  will  first  be  examined  to  ascertain 
whether  the  differences  A  P  (Ref )  —  J  Pt  will  tolerate  the  supposition  that  they  are 
caused  wholly  or  mainly  by  a  constant  error  in  adopted  zenith  point  combined  with  an 
error  in  the  assumed  coefficient  of  sin  Z  in  the  formula  for  flexure.  And  for  the  purpose 
of  assigning  proper  weights  to  A  P(Ref)  —  A  P  in  each  case  e,  will  be  ascertained  by 
approximation.  In  1867  there  are  a  few  observations  of  "miscellaneous  stars"  by 
reflection,  and  as  these  are  situated  almost  exclusively  near  the  zenith  they  will  afford 
additional  evidence  as  to  the  character  of  the  change  near  the  zenith  in  the  value  of 
A  P(Ref )  —  A  P.  The  following  table  exhibits  the  results  from  these  stars  arranged 
in  order  of  zenith  distance  of  stars  observed  directly,  zenith  distances  being  counted 
from  0°  to  360°.  The  first  column  gives  the  name  of  the  star;  the  second  is  P  cor- 
rected wherever  necessary  by  —  ".34,  to  reduce  to  adopted  zenith  points;  the  third 
is  seconds  of  P  (Ref),  reckoned  from  reflected  pole  through  nadir,  etc. ;  the  fourth 
gives  the  number  of  observations  respectively  for  P  and  P  (Ref),  separated  by  a 
hyphen ;  the  fifth  shows  the  respective  weights  on  the  unit  whose  probable  error  is 
1".00.  These  weights  are  deduced  on  the  supposition  that  the  value  of  e,  is  ±  ".25. 
The  sixth  column  shows  the  values  of  P(Ref)  —  P,  and  the  last  column  shows  the 
values  of  Z. 


Name. 

P 

P(Ref) 

Obs. 

71-' 

P(Ref)  —  P 

Z 

B.  A.  C.I  144 

o      '         // 
24    52    46.60 
27    33    15.02 
32    55    18.32 
33    59    05.38 
35    25    36.07 
35    50    31.17 
36    48    07.39 
40    14    03.10 
41    29    61.03 
41    34     11.07 

stars  north  of  zenitl 

46.16 
13.48 
16.99 
05.73 
36.  85 
30.97 
08.28 
02.81 
58.57 
11.36 

,) 

2-1 
1-1 
2-2 
2-1 
2-1 
3-1 
2-1 
2-1 
1-2 
4-1 

2 
1.5 
2.5 
2 
2 
2 
2 
2 
2 
2 

// 

—     .44 
—  1.54 
—  1.33 

+    .35 
+    .78 
—    .20 
+    .89 
—    .29 
—  2.46 
+    .29 

o 
334 
337 
342 
343 
344 
345 
346 
349 
350 
350 

6  Ursae  Majoris  
/3  Ursa  Majoris  
81  Ursse  Majoris  
21  Ursse  Mnjoris  
1  Can.  Ven  
51  Draconis 

o  Auri"fa3 

X  Ursas  Majoris  
z  Hercnlis 

Recapitulation  (t 

20 

-  .39  ±  .23 

344 

*  The  apertnre  of  the  collimators  is  only  2J  inches,  while  that  of  the  telescope  is  8.5  inches. 
AP,-f  .D. 


458 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[52] 


Name. 

P 

P(Ref) 

Obs. 

*? 

P(Ref) 

Z 

15.  A.  C.  4962  

o      /         // 
62    24    32.  79 
62    44    46.97 
63    17    29.45 
64    17    29.63 
65    58    27.  14 
67     19    60.39 
67    47    30.  42 
68    50    40.27 
68    56    22.20 
74    00    47.13 
76    38    37.05 
79    37    07.15 

stars  south  of  zenit 

33.74 
47.64 
28.28 
29.70 
28.04 
59.80 
31.71 
40.  13 
22.  83 
46.32 
36.77 
07.43 

i) 

2-1 
2-1 
2-1 
3-1 
3-1 
2-1 
2-1 
2-1 
2-1 
2-1 
2-1 
2-1 

2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
y 

ti 

+    .95 
+    .67 
—  1.17 
+    .07 
+    .90 
—    .£9 
-|-  1.29 
—    .14 
+     .6:1 
—    .81 
—    .28 
+    .28 

o 
11 
12 
12 
13 
15 
16 
17 
18 
18 
23 
25 
28 

B.  A.  C.  4809  

y    Cor.  Borealis  .  

d    Bootia    

26  Bootis 

B  A  C  1970 

B  A  C  2788 

f    Tauri 

BAG.  5620 

Recapitulation  ( 

24 

+     .  15  ±  .  14 

17 

The  probable  errors  are  deduced  from  the  actual  residuals ;  had  they  been  esti- 
mated from  I  it'  in  each  case,  they  would  have  been  ±  ".22  and  ±  ".20,  respectively,  for 
the  northern  and  southern  groups.  At  about  18°  zenith  distance  on  each  side  there 
are  gaps  without  stars  observed,  more  than  5°  wide  in  each  instance.  Taking  only  the 
stars  nearest  the  zenith,  we  have: — 


7T 

P(Ref)  —  P 

Z 

16  5 

it 
—    27 

o 
346 

[Same,  excluding  %  Ursse  Majoris. 

14.5 

18 

+  .03 

+  .  15 

345] 
15 

The  evidence  in  favor  of  an  abnormal  change  appears  to  be  wanting.  The  result 
has,  however,  but  small  weight.  Collecting  now  all  the  material  which  exists  in  1867 
and  1868  for  determining  A  ZQ7,  A  Z  68,  and  F,  and  collecting  the  values  of  AP  (Ref ) 
—  A  P  into  groups,  including  in  each  group  a  zone  nearly  5°  wide,  we  have  the  fol- 
lowing tables : — 

1867. 


No. 

Meau£ 

AP(Ref)  —  AP 
+  ".16  sin  Z 

v> 

I. 

II. 

III. 

o 

II 

II 

ti 

II 

(D 

309 

—  .54 

15 

—  .49 

—  .13 

+  .11 

(2) 

315 

—  .87 

17 

—  .05 

+  .21 

+  .50 

(3) 

323 

—  .77 

31 

00 

+  .12 

+  .48 

W 

329 

—  .66 

34 

+  .02 

+  .02 

+  .43 

(5) 

334 

—  .56 

31 

+  .03 

—  .07 

+  .39 

(6) 

345 

-•-  .29 

28 

+  .03 

—  .32 

+  .26 

(7) 

350 

—  .81 

22 

+  .67 

+  .21 

+  .84 

(8) 

12 

+  .58 

40 

—  .15 

+  .23 

—  .26 

(9) 

18 

+  .48 

28 

+  .10 

+  .35 

—  .08 

(10) 

25 

+  .49 

50 

+  .25 

+  .35 

.00 

(11) 

32 

+1.01 

46 

—  .11 

—  .16 

—  .44 

(12) 

38 

+1.65 

15 

—  .61 

—  .79 

—1.02 

(13) 

46 

+1.49 

30 

—  .42' 

—  .61 

—  .78 

(14) 

49 

+  .78 

18 

+  .44 

+  .10 

—  .05 

(15) 

53 

+1.13 

6 

+  -17 

—  .24 

—  .36 

[53] 


EEPOET  OP  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


459 


The  correction  +  ".16  sin  #,  in  column  A  P(Eef )  —  A  P,  is  the  reduction  for  differ- 
ence of  latitudes  of  instrument  and  reflecting  surface  in  reflection  observations.  The 
weight,  -',  supposes  =t  l/'.OO  as  the  probable  error  of  the  unit.  By  successive  trials  it 
was  found  that,  taking  c,  =  ±  ".25,  the  assumed  and  concluded  probable  errors  of  unit  of 
weight  in  1868  were  exactly  alike;  and  the  latter  for  1867  was  ±  1".07,  while  from 
the  assumption  it  should  have  been  ±  1".00.  The  approximation  is  considered  quite 
sufficient,  especially  when  it  is  remembered  that  there  is  great  uncertainty  in  the  appli- 
cation of  the  law  adopted  to  represent  /JP(Bef)  — JP.  We  therefore  have  for  any 
given  number  (n)  of  observations  the  weight 

1.00 


The  table  gives  :— 


.0625  +  - 
n 


Values  of  n'  with  arguments  e  and  n. 


E  =  ±  i.oo 


e,  ==  ±  .25 


n 

e  =  ".52 

".54 

".60 

".70 

".80 

'.90 

1".00 

1 

3.0 

2.8 

2.4 

1.8 

1.4 

1.1 

.9 

2 

5.2 

4.8 

4.1 

3.2 

2.6 

2.1 

1.8 

3 

6.6 

6.3 

5.5 

4.4 

3.6 

3.0 

2.6 

4 

7.7 

7.4 

6.6 

5.4 

4.5 

3.8 

3.2 

5 

8.6 

8.3 

7.4 

6.2 

5.  3 

4.5 

3.8 

6 

9.3 

9.0 

8.2 

6.9 

5.9 

5.1 

4.4 

7 

9.9 

9.6 

8.8 

7.5 

6.5 

5.6 

4.9 

8 

10.4 

10.1 

9.3 

8.1 

7.0 

6.1 

5.3 

9 

10.8 

10.5 

9.8 

8.6 

7.5 

6.6 

5.8 

10 

11.2 

10.9 

10.2 

9.0 

7.9 

7.0 

6.2 

15 

12.4 

12.2 

11.7 

10.5 

9.5 

8.6 

7.7 

20 

13.2 

13.0 

12.4 

11.5 

10.6 

9.7 

8.9 

25 

13.6 

13.5 

13.0 

12.2 

11.4 

10.6 

9.8 

30 

14.0 

13.9 

13.4 

12.7 

11.9 

35 

14.'  2 

14.  1 

13.7 

13  1 

40 

14.4 

14.3 

14.0 

13.4 

50 

14!7 

14.6 

14.3 

13.8 

These  can  easily  be  converted  into  any  other  scale  whose  standard  probable 
error  is  e,  by  means  of  the  factor  _.  The  value  of  e  is  found  on  p.  49.  The  weight 

n,  _  *'  (Dir.)  X  *'  (Bef.)  .    taken  to  (he  nearest  unit- 

JT'  (Dir.)  +  -K'  (Kef.) 

Recurring  again  to  the  table  of  comparisons,  ^P(Bef)  —  JP,  (1867),  the  numbers 
in  column  headed  I.  are  the  residuals  (calc.  —  obs.J,  which  result  from  the  employment 
of  the  following  values  deduced  directly  from  the  observations  of  1867,  assuming  that 
the  differences  A  P  (Eef  )  —  J  P  are  due  to  constant  error  and  flexure. 


F=  +  ".74  ±".052. 

The  column  marked  II.  is  constructed  on  the  supposition:  — 
j  Z>  or  A  Z"  =  ^(Bef.)-JP  +  „  M  sin  z. 


460 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


154] 


t.  e.,  assuming  AZio  be  different  for  northern  and  southern  stars,  and  excluding  the 
supposed  flexure,  except  that  of  +  ".06  deduced  from  opposing  collimators.     We  have 
for  northern  stars,  A  Z'  =  —  ".29 ;  for  southern  stars,  A  Z"  =  +  ".40. 
Professor  Newcomb  found*: — 

A  Z'  =  -  ".45     A  Z"  =  +  ".  15. 

The  difference  is  mainly  the  effect  of  the  correction  —  ".34  to  reduce  systematically 
to  zenith  points  derived  from  collimators.  In  the  first  solution  the  small  value  of  AZ 
shows  that  the  zenith  points  thus  derived  are  practically  free  from  constant  error. 

While  the  numbers  in  column  I.  do  not  show  that  agreement  of  fact  with  hypoth- 
esis, which  is  desirable,  they  ought  to  have  some  preference  over  those  of  column  II., 
especially  when  we  consider  that  the  manner  of  usiug  the  corrections  AZ/  and  AZ" ,  is 
at  least  highly  questionable  on  a  priori  grounds.  It  may  be  noted  that  of  the  eight 
comparisons  making  up  line  (7),  we  have: — 


Stars. 

Z 

AP(Ref.)-AP, 
etc. 

w' 

I. 

o 

// 

II 

1st 

4 

349 

—  1.51 

13 

+  1.3 

ad 

4 

352 

-f    .22 

9 

—    .4 

Whatever  the  source  of  these  anomalies  it  is  undoubtedly  quite  irregular  in  its 
action,  and  is  suggested  with  some  probability  by  Faye's  hypothesist  as  to  columns 
of  heated  air  in  the  observing-room,  which  may  principally  or  solely  affect  observations 
by  reflection. 

Explanation  of  column  III.  will  follow  later,  (p.  57). 

We  have  a  similar  table  for  1868: — 


No. 

Mean  Z 

<iP(Ref.)  —  AP 
+  .16  sin  Z 

»r' 

I. 

11. 

III. 

o 

ii 

// 

// 

II 

(16) 

308 

—  .72 

6 

—1.01 

—  .69 

—  .46 

(17) 

3)6 

—  .70 

3 

—  .83 

—  .69 

—  .41 

(18) 

323 

—1.03 

14 

—  .39 

—  .34 

—  .01 

(19) 

328 

—1.75 

20 

+  .42 

+  .40 

+  .77 

(20) 

335 

—1.40 

13 

+  .20 

+  .0(5 

+  .49 

(21) 

345 

—1.14 

10 

+  .13 

—  .16 

+  .37 

(22) 

351 

—1.30 

10 

+  .43 

+  .02 

+  .61 

(23) 

11 

+  .28 

16 

—  .74 

—  .27 

—  .71 

(24) 

18 

+  .23 

20 

—  .55 

—  .22 

—  .57 

25) 

24 

—  .07 

21 

—  .28 

+  .10 

—  .21 

26) 

28 

—  .10 

23 

—  .03 

+  .15 

—  .13 

27) 

33 

—  .51 

23 

+  .47 

+  .£8 

+  .35 

28) 

39 

00 

11 

+  .06 

+  .09 

—  .10 

(29) 

48 

+  .54 

16 

—  .34 

—  .43 

—  .55 

"  P.  six,  Int.  Wash.  Ast.  Obs.,  1867. 
t  Faye,  Comptes  Kendus,  xxi. 


[55J 


KEPO11T  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          461 


The  explanations  under  1867  apply.    We  have  for  I.  :  — 

AZ=—  ".35  ±".035 

F  =  +  ".GO  ±".070 

For  II.  :      AZf=-  ".62  and  AZt'  =  —  ".02. 

The  difference  between  these  numbers  and  those  deduced  by  Newcomb,*  AZ'=  —  ".78  and 
A  Z"  =  —  ".10,  is  probably  due  to  the  changes  in  some  of  the  zenith  points  (see  p.  47,) 
and  in  the  changes  and  additions  produced  by  errata.  There  is  apparently  not  much  to 
choose  between  I.  and  II.  I  shall,  therefore,  proceed  on  the  hypothesis  that  a  portion 
of  the  discordance  in  question  is  due  to  atmospheric,  or  causes  other  than  flexure 
depending  on  sinZ.  Furthermore,  the  method  of  obtaining  value  of  F  by  comparison 
of  direct  and  reflected  observations  of  Z  will  be  considered  as  of  equal  weight  with  the 
method  which  employs  opposing  collimators.  If  we  take  the  mean  by  weights  of  the 
two  values  of  F,  deduced  from  observations  of  1867  and  1868,  we  have  +  ".69,  which 
gives  as  the  mean  by  the  two  methods  :  — 


The  observations  of  1869  are  too  few  to  afford  a  practical  contribution  to  this  result. 
and  those  of  1866  were  deduced  with  a  different  circle. 

By  comparison  of  A  P  68  —  A  P  67  we  shall  have  an  excellent  determination  of  the 
quantities  F'  (or  entire  cosine  flexure)  and  AZ  68  —  J  £67.  To  obtain  most  probable 
values  of  .F,  F',  A  ZG7  and  A  2/68,  it  will  be  best  to  comprise  in  one  set  of  conditional 
equations  all  determinations  which  contribute  to  a  knowledge  of  either  of  the  required 
quantities,  so  that  each  may  exert  its  proper  influence  upon  all  others.  Each  compar- 
ison JP68~  JP67  furnishes  an  equation  of  the  form  AZ67  —  AZ68  +  2  V'cosZ  = 
APQS  —  APG7,  for  direct  observations,  and  J2T67  —  AZ68  +  2  F'cosZ—  —  JP68  + 
J  P67  for  reflected  observations.  The  results  of  1867  and  1868  furnish  247f  such  equa- 
tions of  the  total  weight  908.  Arranging  them  in  the  order  of  zenith  distance  in  zones 
about  5°  in  width,  we  have  38  means  or  groups:^- 

1868^-1867. 


No. 

AP  68  —  AP  67 

Mean  Z 

orAP67(Rcf.) 

7T< 

III. 

—  AP68(Kef.) 

o 

/; 

// 

(30) 

288 

—  .40 

11 

+  .42 

(31) 

294 

—  .57 

22 

+  -47 

(32) 

306 

—  .50 

28 

+  .20 

(33 

311 

—  .33 

23 

—  .04 

(34 

316 

—  1.29 

9 

+  .84 

(35 

323 

—  .86 

30 

+  .32 

(36 

323 

—  .60 

34 

00 

37 

I 

332 

—  .56 

19 

—  .08 

(38 

i 

337 

+  .01 

10 

—  .69 

(39 

I 

345 

—  .88 

16 

+  -If 

(40) 

:;si 

—  .45 

*2 

—  .31 

(41) 

360 

—  .19 

33 

—  .58 

*  P.  xx,  Int.  Wash.  Ast.  Obs.,  1868. 

t  The  comparisons  of  a  Cassiop.,  8,  P.,  aud  a  Cephei,  S.  P.,  are  rejected  as  of  small  weigbt. 


462 


UNITED  STATES  NORTHERN    BOUNDARY  COMMISSION. 


|5ti] 


1868-1867— Continued. 


No. 

MeanZ 

A7J  68  —  AP  67 
orAP67(Ref.) 
—  APC8Eef.) 

*•' 

III. 

o 

// 

fl 

(42) 

7 

—  .86 

22 

+  .10 

(43) 

11 

—  1.17 

40 

+  .42 

(44) 

17 

—  .83 

44 

+  .11 

(45) 

•21 

—  .86 

26 

+  -I? 

(46) 

24 

—  .71 

50 

+  .04 

(47) 

29 

—  .89 

60 

+  .26 

(48) 

33 

—  .42 

72 

—  .16 

(49) 

40 

—  .06 

43 

—  .44 

(50) 

47 

—  .U 

65 

+  .02 

(51) 

69 

—  .  55 

24 

+  .24 

(5,') 

59 

+  .58 

23 

—  .79 

(53) 

64 

—  .05 

16 

—  .08 

(54) 

69 

+  .92 

7 

—  .96 

(55) 

231 

+  .66 

6 

+  .44 

(56) 

224 

+  .OJ 

3 

+  1.17 

[57) 

217 

+  .41 

18 

—  .12 

58) 

210 

+  .82 

14 

—  .46 

59) 

205 

+  .31 

17 

+  .10 

60) 

195 

+  .63 

10 

—  .15 

' 

61 

169 

+  .21 

12 

+  .29 

l 

62 

168 

+  .13 

13 

+  .36 

63 

161 

-.-    +  .22 

12 

+  .24 

64 

155 

+  .34 

20 

+  .08 

65 

148 

+  1.86 

21 

—  .52 

66 

140 

+  1.10 

6 

+  .15 

[67) 

132 

+  1.21 

13 

—  .07 

Finally  we  have  from  opposing  collimators : — 

F  K1  " 

(68)  +".06  G20  +.32; 

where  n'  is  determined  a  posteriori  iu  such  a  manner  that  it  shall  be  equal  to  one-half 
the  weight  of  F  in  the  solution  of  normal  equations. 

Representing  by  —  n,  for  convenience,  the  numbers  in  third  column  (in  the  three 
tables),  we  have  the  forms: — 

(1867)  {2J£67  +  2.F  sin 

(1868)  {2  J.Z63  +  2  F  sin 
(1868-3867)     {  AZ  67  -  ^#68  +  2  F'  sin  Z 

IF _  ".06  =  0  j-/  620 

The  solution  of  numerical  equations  formed  in  accordance  with  the  above,  leads  to 
these  normal  equations. 

AZ68+  904.6  .F  +  100.0 
-  904.6  +  94.2 
+  2493.!) 

+  1255.5 
+  ".082   ±  ".024 
A  Z  08  =  -  ".290  ±  ".030 
F     =  —  ".571   ±  ".024 
F      =  +  ".381  [±  ".030 J 
E=  ±  1".<)7 


2552.0  AZ  67-    908.0 

—    908.0  +1756.0 

+    904.6  —    904.6 

+    100.0  +     94.2 

The  solution  gives, — 


F+  5.71=0 
+  31.59  =  0 
+  1088.08  =  0 
-  459.40  =  0 


[57]  REPORT  OP  T1IE  CHIEF  ASTRONOMER,  APPENDIX  H.          463 

It  is  hardly  necessary  to  remark  that  the  probable  error  as  applied  to  F  lias  no 
significance;  but  if  we  admit  that  the  anomalous  conditions  affecting  J  P(Ref)  —  J  P 
acted  with  tolerable  uniformity  in  1807  and  1868,  then  the  probable  error  of  the  value 
of  F'  is  quite  real.  The  value  of  E  is  unfavorably  influenced  by  the  introduction  of 
equation  (68).  Using  (as  in  other  cases)  the  separate  residuals  making  up  groups  (30) 
to  (54)  inclusive,  we  have 


and  from  groups  (55)  to  (67)  inclusive 


The  agreement  of  E  with  assumed  value  is  all  that  could  be  desired. 

The  numbers  in  column  III.  are  the  residuals  arising  from  the  adoption  of  the 
above  values  in  the  individual  equations.  From  groups  (30)  to  (67)  there  are  no 
evidences  of  large  outstanding  errors  of  a  systematic  nature  ;  nor,  with  one  or  two 
exceptions,  of  residuals  larger  than  should  be  expected  from  the  weights.  Small  errors 
in  the  division  correction  doubtless  exist,  and  it  is  to  me  matter  of  surprise  that  these 
groups  are  so  well  represented  by  the  simple  law  assumed.  So  much  cannot  be  said 
of  the  first  29  groups.  The  outstanding  residuals  in  column  III.  may  be  attributed  to 
atmospheric  disturbances,  to  error  in  assumed  value  of  -F,  and  to  other  possible 
causes,  whose  existence  is  not  clearly  defined. 

It  will  be  assumed  that  the  difficulty  is  mainly  with  the  reflection  observation  ; 
and  these  will  accordingly  be  excluded  from  all  further  participation  in  the  definitive 
results  for  1867  aud  1868.  Assuming  the  correctness  of  F,  the  value  of  A  Z  69  will  be 
deduced  from  the  comparison  of  direct  and  reflected  observations  of  1869,  given  on 
p.  xxiii,  Int.  Wash.  Ast.  Obs.  Reversing  the  signs  in  column  "D  —  R",  correcting 
by  —  .64  sin  #,  and  taking  one-half  the  mean  by  weights  of  the  outstanding  residuals, 

we  have  :  — 

+  ".44  ±  ".06. 


The  circle  was  shifted  at  the  beginning  of  the  year  30'  relatively  to  the  telescope. 
In  computing  flexure,  no  account  was  taken  of  this  circumstance. 

The  observations  of  1865  afford  no  opportunity  for  independent  determination  of 
the  cosine  flexure  of  the  circle  used  .  AZ&Q  and  the  sine  flexure  (F)  were  found  by 
Professor  Newcotnb  from  comparison  of  direct  and  reflected  observations.*  The 
values  were  — 

J  Z  66  =  -  ".72 
=  -".78 


The  result  of  the  investigation  for  .F66  in  the  volume  for  1865  is  —  1".12  ;  and  this  was 
adopted  in  the  reductions.    I  have  adopted  the  mean  of  the  two  results 

F  66  =  -  ".95 

The  mean  by  weights  of  A  P  67  and  J  P  68  corrected  for  J  Z,  F  and  F1  was  then  taken 

*  Introduction  to  Washington  Astronomical  Observations  for  1866,  p.  xxiii. 


464 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[58] 


as  standard,  with  which   A  P  66,  corrected  by  —  ".72  —  ".95  sin  Z  was  compared. 
Arranged  in  convenient  groups  the  results  are  these : — 


Group. 

MeanZ 

A  F  I  68  \  (corrected) 
—  A  P66  (corrected). 

n1 

Calc.  —  obs. 

o 

// 

n 

(1) 

293 

—  .14 

24 

+  .06 

(2) 

307 

—  .07 

32 

—  .03 

(3) 

312 

+  .12 

44 

—  .22 

(4) 

325 

+  .02 

70 

—  .13 

ffi 

334 

—  .25 

35 

+  .14 

(6) 

349 

—  .02 

50 

—  .10 

(7 

2 

—  .25 

67 

+  .13 

(8) 

13 

+  .02 

112 

—  .14 

9 

23 

—  .03 

150 

—  .09 

(10) 

32 

+  .01 

1G6 

—  .12 

(11) 

44 

—  .35 

150 

+  .25 

(12) 

55 

—  .37 

62 

+  .28 

(13) 

65 

—  .38 

42 

+  .29 

(14) 

228 

—  .22 

21 

+  .20 

(15) 

214 

+  .19 

37 

—  .20 

(16) 

206 

+  .15 

28 

—  .16 

(17) 

192 

+  .10 

35 

—  .10 

(18) 

165 

—  .37 

30 

+  .37 

(19) 

153 

+  .20 

38 

—  .21 

(20) 

140 

.00 

14 

—  .01 

(21) 

132 

—  .02 

22 

00 

The  results  from  (14)  to  (21)  are  from  reflection  observations.  The  numbers  in 
third  column  are  too  small  and  too  irregular  to  exhibit  any  decided  preference  for  a 
given  law.  It  will  be  assumed  that  the  above  value  of  J  £66  requires  correction,  and 
that  a  term  should  be  introduced  for  cosine  flexure.  I  have  found  :  — 

—  ".06  [±  .04]  —  ".06  [±  .04]  cos  Z. 

The  residuals  in  the  last  column  are,  on  the  whole,  very  satisfactory.  Those  in 
(11),  (12),  and  (13),  however,  show  a  slight  tendency  to  deviation  from  the  assumed 
law.  We  have  arrived  at  the  following  corrections  to  J  P,  which  are  adopted. 

1866.  —  .78  —  .95  sin  Z  —  .06  cos  Z 

1867.  +.08  +  .38sin£-.57cos£+{IrriS1tasr  Correction  for  error  of  zenith  J 

1868.  —  .29  +  .3  4  sin  Z  +  .57  cos  Z  +  {  Irregular  corrections.  } 

1869.  +.44  +  .38  sin  Z  —  .57  cos  Z 

or  more  conveniently  : 


1866.     —  .78  -.95  sin  {  312.5  +  P\ 
(A)          1867.     +  .08  +  .69  sin  j  252.6  +  P  }  +  etc. 
1868. 
1869. 


—  .29  +  .69  sin  {     5.2  +  P  \  +  etc. 
+  .44  +  .69  sin  j  252.6  +  P  } 

These  corrections  are  applicable  to  polar  distances  from  direct  observation. 


[59] 


EEPOET  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          465 


Latitude  and  Refraction. 

In  this  series  of  observations,  there  is  uo  material  for  examining  the  correctness 
of  the  adopted  temperature  coefficient  of  atmospheric  expansion.  Owing  to  the  low 
elevation  of  the  pole  and  the  deficiency  of  observations  at  low  altitudes  of  stars  at 
lower  transit,  the  determination  of  an  independent  constant  of  refraction  is  likewise 
out  of  the  question.  The  process  of  obtaining  A  <p  may  be  briefly  summarized. 

All  polar  distances  by  direct  observation  in  each  of  the  years  were  corrected  by 
(A)  ;  and  supposing  the  differences  between  corrected  polar  distances  of  the  same  star 
from  upper  and  lower  culmination  to  be  due  to  error  of  assumed  latitude  and  refrac- 
tion constant,  we  have  — 


A  P  (U.  C.)  corrected  )       „  . 
+  AP  (L.  O.)  corrected  }  :    2  A  V  ~  (P  + 


The  results  of  all  the  years  combined  in  one  set  of  equations,  and  arranged  in  con- 
venient groups  following  the  order  of  polar  distance,  are  these  : 


No. 

V 

Calc.  —  obs. 

Stars'  name,  or  num- 
ber of  stars. 

(1) 

//             // 
2   A6  —  143  k  +  .  69  =  0 

14 

it 
—  .07 

h    Ursse  Minoris. 

(2) 

2          —  143    +  .60 

29 

—  .16 

a    Ursse  Minoris. 

(3) 

2          —  144    +  .75 

15 

—  .01 

51  (H)  Cephei. 

(4) 

2          —  144    -H.09 

22 

+  .33 

6    Ursse  Minoris. 

(5) 

2          —  150    +1.08 

10 

+  .32 

3 

(6) 

2          —  1G2    +  .  66 

29 

—  .10 

5 

(7) 

2          —  171     +  .85 

31 

+  .09 

7 

(8) 

2          —  185    -j-  .78 

13 

+  .01 

3 

(9) 

2          —  202    +  .30 

21 

—  .47 

4 

(10) 

2          —  210     +  .72 

8 

—  .05 

5 

(H) 

2          —  227    +  .  91 

16 

+  .14 

4 

(12) 

2         —  236    +  .  95 

5 

+  .IS 

1 

(13) 

2          —  256    +1.23 

4 

+  .45 

2 

(14) 

2         —  320    +.  88 

4 

+  .09 

1 

The  coefficients  of  fc  are  taken  at  their  mean  values  for  the  mean  temperature  at 
Washington,  those  from  (11)  to  (14)  excepted,  which  are  for  lower  culmination  taken 
from  the  detailed  observations.  From  the  above  equations  result  — 


A<?  =  -  ".369 
fc  =  +    .00014 


".105  ;  or  -  ".38  +  8C".9  fc 
±    .00119 


{Bessel's  refractions}  x  .99986  =  Washington. 

The  probable  error  of  k  is  thus  nearly  10  times  the  quantity  itself,  and  as  the 

change  in  refraction  would  be  practically  insignificant,  uo  use  is  made  of  it.    The 

probable  error  of  A  <p  is  with  respect  to  the  uncertainty  of  fc.    Assuming  fc  to  be  with- 

out error  the  probable  error  of  A  <e  becomes  ±  ".03.    To  get  the  deviations  from  A  y>  the 

N  B  -  30 


466  UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.  [60] 

numbers  in  column  "Calc.  —  obs."  must  be  divided  by  2.    Excluding  all  observations 
where  Z  >  75°,  the  results  of  separate  years,  for  latitude  are: 

//        // 

1866  -  .46  ±  .08 

1867  —  .26  ±  .06 

1868  -  .46  ±  .06 

1869  -  .22  ±  .12 
Mean  by  weights  —  .37 

The  differences  are  not  much  greater  than  the  probable  errors  would  lead  us  to 
expect,  especially  when  we  consider  the  uncertainty  of  J  Z  for  each  year. 

The  adopted  latitude,  38°  53'  38".43,  is  more  than  0".8  less  than  that  found  in 
1845,*  with  the  mural  circle,  and  ".35  less  than  the  result  with  the  same  instrument  in 
1861-2-3-4.t  The  difference  between  the  earliest  and  latest  determination  is  appar- 
ently greater  than  the  sum  of  any  probable  instrumental  errors  in  the  two  series.  If 
the  flexure  from  opposing  collimators  had  been  adopted,  the  seconds  of  latitude  would 
have  been  38".  66  very  nearly.  If,  on  the  other  hand,  we  take  the  results  of  comparison 
of  Me  68  with  Wn  68,  and  suppose,  accordingly,  that  the  refractions  of  the  latter  ought 
to  be  multiplied  by  .9953  the  seconds  of  latitude  are  38".83  ;  leaving  a  difference  not 
accounted  for  of  ".42  ;  and  this,  too,  under  the  extreme  supposition  that  the  refractions 
of  1845  are  correct,  while  the  same  refractions  for  1868  need  to  be  multiplied  by  .9953. 

Combining  with  table  (A)  the  correction  +  ".37,  for  —  A  q>  already  determined,  we 
arrive  at  the  following  definitive  correction  to  P  and  A  P: 

n         a 

1866  -  .41  —  .95  sin  (312.5  +  P) 

1867  +  .45  +  .69  sin  (252.6  +  P)  +  j  —  ".34  to  nadir  values  of  P  and  A  P.  j 

(B)     isfis  fit*  «-n/     ^9-L.P^.i.J   Irregular    corrections    for  error  of 

+  .08  +  .69  sin  (    5.2  +  P)  +  4 


pointg     gee 
1869        +  .81  +  .69  sin  (252.6  +  P) 

Column  (B)  of  the  subjoined  table  is  constructed  from  these.  In  column  "Final" 
are  found  the  systematic  corrections  necessary  to  reduce  the  North  Polar  Distances,  after 
they  are  first  corrected  for  division  error  and  error  of  certain  zenith  points,  to  the  Nor- 
mal System  of  this  paper.  It  is  formed  by  subtracting  from  (B)  the  declination  cor- 
rection of  Wn  68,  taken  from  Table  IX. 

"Appendix  to  Washington  Astronomical  Observations  for  1845. 
1  Appendix  to  Washington  Astronomical  Observations  for  1864. 


[01]  REPORT  OP  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          467 

Wn  GG-  Wn  GO.     Table  of  corrections  to  Polar  Distances  by  direct  observation.* 


136G. 

1867. 

1868. 

18G9. 

P 

(») 

Final. 

(£) 

Final. 

(JB) 

Final. 

(») 

Final. 

o 

// 

// 

// 

// 

// 

// 

// 

// 

3155 

+  .50 

+  .70 

—  .05 

4-  .15 

—  .15 

4-  .05 

+  .30 

+  .50 

340 

+  .47 

+  .62 

—  .09 

4-  .06 

—  .10 

+  .05 

+  .^.'6 

+  -41 

345 

+  .43 

+  .53 

—  .13 

—  .03 

—  .04 

+  .06 

+  .23 

+  .33 

350 

-f-  .39 

+  .44 

—  .16 

—  .11 

4-  .02 

4-  .07 

+  .20 

+  .25 

355 

+  .34 

4-  .36 

—  .18 

—  .16 

+  .08 

+  .10 

+  .17 

+  .19 

3GO 

+  .29 

+  .29 

—  .20 

—  .20 

+  -14 

+  .14 

+  .15 

+  .15 

5 

+  .23 

4-  .21 

—  .21 

—  .23 

4-  .20 

+  .18 

+  .  14     |     +  .  12 

10 

+  .17 

+  .12 

—  .23 

—  .28 

+  .26 

+  .21 

+  .13 

+  .08 

15 

+  .10 

00 

—  .23 

—  .33 

4-  .32 

+  .22 

+  .12 

+  .02 

20 

+  .03 

—  .12 

—  .23 

—  .38 

4-  .37 

4  .22 

4-  -13 

—  .03 

25 

—  .04 

—  .24 

—  .23 

—  .43 

+  .43 

+  .23 

+  .13 

-  .07 

30 

—  .12 

—  .38 

—  .22 

—  .48 

+  .48 

4  .22 

+  -14 

-  .  12 

35 

—  .20 

—  .52 

—  .20 

—  .52 

4-  .52 

+  .20 

+  .15 

—  .  17 

40 

—  .28 

—  .64 

—  .18 

—  .54 

+  .57 

+  .21 

+  .17 

—  .19 

45 

^  37 

—  .76 

—  .16 

—  .55 

+  .61 

+  .22 

+  .£0 

JC) 

50 

—  !  45 

—  .87 

—  .13 

—  .55 

4-  .64 

+  .22 

4-  .22 

—  .'so 

55 

—  .53 

-  .93 

—  .09 

—  .54 

+  .<?8 

+  .23 

+  .26 

—  .19 

60 

—  .62 

—1.09 

—  .05 

—  .52 

+  .70 

4-  .23 

-j-  .30 

—  .17 

65 

—  .70 

—1.20 

—  .01 

-  .51 

4-  .73 

+  .23 

+  .34 

—  .16 

70 

—  .77 

—1.30 

+  .03 

—  .50 

+  -74 

+  .21 

4-  .39 

-  .14 

75 

—  .85 

—1.40 

-j-  .08 

—  .47 

4-  .76 

+  .21 

4-  .44 

—  .11 

80 

—  .92 

—1.49 

+  -14 

—  .43 

+  .76 

+  .19 

+  .49 

—  .08 

85 

—  .99 

—1.57 

+  .19 

—  .39 

+  -77 

+  .19 

4-  .55 

—  .03 

90 

—1.05 

—1.64 

+  .25 

—  .34 

4-  .76 

+  .19 

+  .60 

+  .01 

95 

—1.11 

—1.70 

+  .30 

—  .29 

+  .76 

+  .19 

+  .66 

+  .07 

100 

—1.16 

—1.76 

4-  .36 

—  .24 

+  .74 

4-  .14 

+  .72 

+  .12 

105 

—1.21 

—1.84 

+  .42 

—  .21 

+  .72 

+  .09 

+  .78 

+  .15 

110 

—1.25 

—1.95 

+  .48 

—  .22 

+  .70 

00 

+  .84 

+  -14 

115 

—1.29 

—2.09 

+  .54 

—  .26 

+  .67 

—  .13 

+  .90 

+  .10 

120 

—1.32 

—2.25 

+  .60 

—  .33 

+  .64 

—  .29 

+  .96 

+  .03 

125 

—1.34 

—2.43 

+  .66 

—  .43 

4-  .60 

—  .49 

+1.01 

—  .08 

*  An  explanation  of  the  difference  between  the  corresponding  numbers  contained  in  columns  "  (B)" 
and  "Final"  is  suggested  in  the  comparison  of  Washington  and  Melbourne  polar  distances.  (See  pp. 
66  to  68.) 


468 


UNITED  STATES  NOETHEEN  BOUNDARY  COMMISSION. 


[62] 


With  the  corrections  in  column  (J5),  and  the  table  of  weights,  on  p.  53  the  follow- 
ing catalogue  is  constructed,  which  appears  to  require  no  explanation,  except  that  the 
definitive  declinations  converted  from  N.  P.  D.  are  first  given,  followed  by  their 
respective  weights;  and  after  these  the  seconds  of  declination  converted  in  like,  man- 
ner for  separate  years : 

Wn  68 Catalogue. 


A  1  Bfift  0 

188< 

>. 

1867. 

186 

3. 

186 

3. 

d 

a1 

6         n' 

a 

*' 

S 

_/ 

a    Androiuedse 

O        /           /' 

4-  28  21  41  36 

44 

n 
41.6 

11 

n 
41  4     12 

a 

41  7 

10 

II 
40  7 

9 

y    Pegasi  

+  14  26  57.  84 

45 

58.4 

19 

58.  0     14 

56  9 

10 

57  9 

q 

a    Cassiopea3 

+  55  48  45.69 

23 

45  9 

fi 

45  9      8 

45  6 

7 

44  6 

a 

(3    Ceti  

—  18  42  42.44 

34 

42.1 

11 

42.  2    12 

43.1 

q 

42  9 

2 

21  Cassiopeas  

+  74  15  57.  51 

38 

57.6 

7 

56.2      3 

57  5 

«i 

21  Cassiopeaa,  S.  P  

58.3 

6 

57.3      8 

57  1 

*; 

58  1 

4 

e     Piscium  

4-    7  10  42.  72 

35 

43.0 

14 

42.  6    12 

42  4 

q 

v     Piscium  

4-  26  34  08.94 

7 

08.  9      7 

a    Uri-sB  Minoris  

4-  88  36  20.  33 

112 

20.7 

15 

20.  2    15 

20  2 

14 

19  9 

1° 

a    Ursse  Mirjoris  S.  P.  .  

20.4 

TS 

20.  3    15 

20  2 

11 

20  7 

13 

6    Ceti  

—    8  51  55.48 

28 

55.6 

10 

55.  4     10 

55  4 

R 

A   Cassiopeaa  

4-  69  35  02.  07 

3 

02  1 

S 

i?    Piscium  

+  14  39  51.  18 

39 

51.3 

11 

50  7     14 

51  3 

10 

52  6 

0 

o     Piscium  

+    8  29  31.  44 

32.3 

11 

30  9    13 

31  2 

10 

31  5 

3 

j3    Ariel  is  

4-  20  09  41.  09 

41 

41.4 

II 

40  3    13 

41  2 

q 

42  0 

5 

50  Cassiopeos  

+  71  46  49.78 

31 

50.6 

8 

49  1      3 

51  0 

S 

49  5 

0 

50  Cassiopeas,  S.  P  

48.6 

/\ 

49  9      5 

49  4 

<i 

49  5 

0 

a.    Arietis  

+  22  EO  12.29 

47 

12.5 

11 

12  1     14 

12  1 

q 

12  5 

10 

f    Ceti  

+    8  13  33.  38 

32 

33.9 

8 

33  3    12 

33  3 

q 

33  0 

T 

£     Ca^siopeaB  

4-  66  48  22.  85 

17 

23.4 

6 

22  2      3 

22  6 

6 

23  0 

0 

y    Ceti  

-f-    2  40  39.92 

31 

40.0 

10 

40  1    12 

39  9 

7 

38  8 

2 

T    Persei  -  

4-  52  13  12.48 

3 

12  5      3 

a    Ceti  

4-    3  34  12.  14 

38 

12.7 

V> 

12.  2    13 

12  2 

8 

10  5 

5 

Cephei(48H)  

4-  77  14  42.20 

41 

41.8 

7 

42  0      5 

42  5 

7 

Cephei  (48  H.)  S.  P  

42.8 

7 

42  1      7 

41  5 

6 

43  5 

2 

C     Arietis  .                ..           ..... 

4-  20  33  11.28 

27 

11.6 

8 

11  0    10 

11  3 

7 

11  3 

2 

n    Persei  

4-  49  23  18.20 

24 

18.5 

10 

18  4      7 

17  5 

5 

17  6 

0 

(5    Persei  . 

4-  47  21  43  94 

8 

43  3 

Q 

46  0 

2 

ri    Tauri  

4-  23  41  39.92 

36 

40.1 

10 

40  1    12 

39  9 

q 

39  1 

5 

f     Persei  

4-  31  29  19.16 

18 

18  8 

fi 

17  9      5 

20  4 

7 

•y1    Eridani  

—  13  53  10.10 

25 

10.5 

q 

10  3      7 

09  6 

7 

09  1 

2 

y    Tauri  

+  15  18  22.20 

30 

21.8 

q 

22.  1     12 

22  5 

7 

23  7 

0 

e     Tauri  

4-  18  53  05.69 

32 

05.7 

7 

05.7      2 

05  9 

11 

05  4 

10 

«    Tauri  

+  16  14  28.  12 

45 

28.1 

11 

28.  2    14 

28  4 

10 

27  7 

8 

a    Caaielopardalis  .   .  

4-  60  06  49.  30 

19 

49.4 

7 

49.0      5 

49  4 

1 

49  5 

? 

i     Aurigae  .  ...  

4-  32  57  13.72 

36 

13.8 

q 

13.  8    12 

14  1 

8 

13.0 

7 

11  Orionia.     .  

4-'  15  13  02.29 

26 

02.9 

q 

02.0      9 

01.6 

6 

03  0 

<> 

a    Auriga).   .  .-     

4-  45  51  36.35 

16 

36.5 

4 

36.  0      5 

35.8 

5 

38  3 

0 

/3    Orionis     ...  .  .  

—    8  21  23.54 

35 

23.4 

11 

23.  8    12 

22.9 

7 

24  4 

•\ 

/3    Tauri  

4-  28  29  33.98 

44 

34.2 

11 

34.  0    13 

33.9 

11 

33  7 

7 

Groombridge  986  

4-  74  56  58.  71 

5 

57.7 

3 

Groombridge  966,  8  P  

60.3 

f 

<J    Orionis  .  .  .  

—    0  23  58.  43 

34 

58.6 

10 

58.  0    11 

58.3 

7 

59.0 

6 

—  17  55  09.93 

2 

09  9 

0 

E     Orionis  ..  ..  .  

—    1  17  20.  12 

36 

19.7 

1° 

20.  3    11 

20.4 

8 

20.1 

<i 

a    Columbss  .  .. 

—  34  08  47.  58 

8 

47.8 

1 

48.0 

4 

47.0 

T 

a    Orionis  .  .  .  

4-    7  22  46.  37 

42 

46.6 

14 

46.  3    13 

46.6 

7 

45.9 

8 

[03]  REPORT  OF  THE  CB1EF  ASTEONOMEE,  APPENDIX  H.          469 

Wn  68 Catalogue — Continued. 


A   1  h'fW  ft 

T/ 

186 

6. 

186 

7. 

186 

8. 

18C 

9. 

6 

V1 

t 

*> 

6 

a> 

& 

IT' 

Camclopardalis  (22  H)    

o     /        // 
+  69  21  38  95 

12 

a 

n 

n 
39  7 

6 

n 
38  2 

6 

[i    Geiuinoruffl.  ...  

+  22  34  41.69 

26 

41.7 

10 

41.6 

8 

41  6 

4 

41  9 

4 

+  16  30  32.  63 

46 

32.7 

11 

32.3 

13 

3.3  0 

g 

32  7 

11 

Cepbei  (51  H)  

-f-  87  14  28.83 

68 

29.0 

T' 

28  5 

V> 

29  4 

7 

28  4 

7 

Cephei  (51  H.)  S.  P  

28.8 

1° 

29  4 

8 

28  5 

10 

28  47  40  55 

32 

40  3 

10 

40  3 

9 

41  2 

5 

40  7 

g 

—  •  26  11  08  42 

15 

07  8 

7 

08  9 

7 

09  2 

1 

A    Geminorum.  ..  .-  ..... 

—  16  46  30.87 

3 

30.9 

T 

+  22  13  20.  62 

42 

20.7 

11 

20  4 

1° 

20  2 

9 

21  1 

10 

Pi.  VII  67  

-(-  68  43  50.  22 

8 

51  4 

0 

49  8 

6 

o2  Geniiuorum..  .  ...  ....  

+  32  10  20.41 

41 

28.9 

11 

29  7 

11 

29  4 

11 

29  8 

g 

£?    Geminorum   -.  

+  28  20  32.07 

48 

31.9 

11 

32  2 

n 

32  2 

12 

32  0 

9 

0    Geminorum.  ........  .  

+  27  06  16.71 

35 

16.4 

8 

16  2 

9 

17  3 

g 

17  0 

10 

Ursse  Majoris  (3  H)  

-f  68  51  30.47 

2 

30  5 

2 

15  Argus          .  

—  23  55  32.28 

30 

32  9 

4 

32  4 

11 

31  5 

g 

32  3 

9 

+    6  54  03.44 

39 

03.3 

7 

03  7 

T> 

03  5 

9 

03  3 

11 

+  48  33  27  60 

23 

27.7 

4 

28  1 

<i 

27  4 

8 

27  4 

(j 

o"3  Ursse  Majoris  ..........  

+  67  40  02.77 

21 

02  8 

1 

02  9 

8 

02  8 

4 

02  6 

6 

4-  11  11  50.66 

37 

50.0 

7 

50  9 

10 

50  7 

10 

50  9 

10 

a     Lyncis  .     ..  .  .  .  

-)-  34  56  55.34 

8 

55  3 

8 

Draconis  (1  H)  

+  81  54  20  17 

20 

19  6 

6 

21  8 

3 

Draconis  (1  H.)  S.  P  

19  9 

7 

20  3 

4 

a    Hydraj           .  .  

—    8  05  17  06 

39 

17  2 

10 

16  6 

IS 

17  4 

q 

17  3 

7 

4-  70  24  27  62 

3 

27  6 

3 

4-  52  16  36  96 

37  0 

5 

4-  24  22  49  38 

36 

49  4 

11 

49  3 

n 

48  4 

3 

49  8 

9 

4-  26  37  37  42 

32 

38  2 

8 

37  4 

10 

38  0 

4 

36  6 

10 

a     Leouis  .  .....  

4-  12  36  39  55 

45 

39  7 

n 

39  6 

11 

39  1 

g 

39  7 

10 

32  Ursse  Majoris  .  ......  ... 

4-  65  45  54  91 

10 

55  0 

4 

54  8 

6 

-f  20  30  28  65 

42 

29  1 

11 

28  2 

is 

28  5 

8 

28  9 

10 

Draconis  (9  H)  

4-  76  23  29  48 

32 

29  1 

i 

29  4 

5 

29  9 

4 

29  3 

6 

Draconis  (9  H.)  S.  P  

29.8 

7 

29.3 

6 

p    Leonis.  ..  

+    9  59  04  99 

35 

05  1 

q 

05  0 

10 

05  3 

q 

04  4 

7 

i     Leonis  ...  .....  . 

4-  11  14  34  02 

36 

34  1 

11 

33  4 

q 

34  6 

8 

34  0 

g 

/3    UrssB  Majoris  .  .. 

+  57  05  20  36 

5 

20  4 

5 

+  62  27  46  23 

30 

45  1 

7 

46  1 

11 

47  1 

5 

46  9 

7 

4-  21  14  46  61 

41 

46  8 

1° 

46  4 

11 

47  0 

6 

46  3 

9 

—  14  03  53  33 

29 

53  2 

6 

53  4 

11 

52  3 

5 

54  2 

7 

4-    3  34  57  95 

31 

f-7  5 

H 

58  3 

11 

59  5 

3 

57  5 

9 

/t    Draconis  ...  .  

4-  70  03  33  15 

28 

3-2  6 

7 

33  3 

10 

34  o 

6 

32  7 

5 

v     Leouis  ......         ......... 

—    0  05  43  50 

34 

44  5 

q 

43  3 

11 

42  5 

5 

43  3 

9 

X    Ursas  Majoris    ....         .... 

4-  48  31  39  10 

3 

39  1 

<i 

/}    Leouis  ......     ..... 

4-  15  18  34  72 

44 

34  7 

11 

34.8 

11 

34  7 

8 

34  8 

9 

4-  54  25  42  87 

31 

42  8 

7 

42.5 

11 

43  6 

7 

42  7 

6 

o     Virginia    .  .           ... 

-+-    9  27  57.92 

35 

58  0 

10 

57.6 

11 

58  4 

f, 

57  8 

8 

Draconis  (4  H)  ._  ...... 

4-  78  20  59  70 

37 

59.7 

fi 

59.4 

10 

59  9 

7 

59.7 

4 

Draconis  (4  H.)  S.  P  

60  3 

4 

59.8 

/I 

59  1 

0 

ij    Virginis  .  ...  ..   

+    0  04  00  19 

36 

59.6 

11 

60.3 

1° 

61  4 

5 

60  2 

8 

22  39  59  66 

33 

59  7 

11 

59  6 

9 

59  4 

5 

59  9 

g 

K    Draconis  .  .  . 

4-  70  30  58  53 

14 

58.7 

0 

58.2 

5 

58.8 

<\ 

58  7 

3 

Camelopardalis  (32  H)  . 

+  84  07  50  03 

27 

51.6 

4 

49.4 

q 

50.5 

5 

49.9 

3 

Camelopardalis  (32  H.)  S.  P 

49  6 

6 

a    Canum  Venaticorum  ..  . 

4-  39  01  54.03 

46 

54.1 

n 

54.0 

14 

53.8 

I9 

54.0 

7 

0    Virginis  

—    4  50  01  45 

34 

01.3 

q 

01.8 

10 

01.3 

6 

01.3 

q 

470          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.  [64J 

W n  G8 Catalogue — Continued. 


A  i  Hfift  n 

ir' 

186 

3. 

186 

r. 

186 

3. 

186 

3. 

<S 

TT' 

6 

^ 

6 

IT' 

(5 

is' 

O       '          " 

—  10  28  17.23 

48 

II 

17.4 

14 

n 
17.5 

14 

n 
16.7 

11 

// 
17.1 

q 

+  55  36  56.  49 

7 

56.5 

7 

+    0  04  47.43 

42 

47.2 

is 

48.6 

T> 

47.0 

in 

46  6 

7 

+  56  01  31.  96 

5 

32.0 

B 

B.A.  C.  4596  

+  41  45  05.79 

8 

05.8 

8 

77    Bootis  .,__..  ......  ...... 

+  19  Oil  37.23 

44 

37.0 

14 

37.1 

13 

37  6 

10 

37  5 

7 

77    Ursro  Majoris  ....  ..   ....... 

+  49  58  22.25 

32 

22.7 

8 

22.0 

1° 

23.0 

7 

21  3 

B 

11  Bootis  

+  28  01  31.  09 

7 

31.1 

7 

a    Draconis    ...... 

+  65  00  26.27 

26 

25.6 

fi 

26.  6 

C) 

26.9 

l\ 

26  0 

7 

4-  25  43  04.59 

7 

04  6 

7 

a     Boo"  is..   ..........   . 

+  19  52  14.  46 

48 

14.8 

11 

14  5 

n 

14  3 

12 

14  1 

q 

6     Bootis  ........ 

+  52  27  41.90 

22 

41  6 

6 

42  1 

q 

41  4 

4 

42  7 

T 

y    Boot  is......  ..... 

+  38  53  13.  10 

5 

13  1 

5 

5    Ursae  Minoris  .              .  . 

+  76  16  57.98 

38 

57  1 

8 

58  3 

q 

59  3 

7 

56  8 

fi 

5    TJrero  Minoris,  S.  P  

58.7 

<> 

58.4 

fi 

B.A  C  4827  

-f-  47  21  56.77 

g 

56  8 

8 

e1    Bootis     .           .     . 

+  27  37  E5.24 

45 

55  3 

T> 

55  2 

14 

55  7 

10 

54  6 

q 

(i3  Librse         .                ..... 

—  15  29  29.70 

38 

29  8 

11 

29  6 

11 

29  6 

8 

29  8 

8 

B.A.C.4897  

+  38  21  22.  96 

7 

23.0 

7 

+  74  41  41  58 

48 

42  4 

8 

41  6 

11 

41  8 

7 

41  4 

8 

P    Ursae  Minoris,  S.  P.  ......  .... 

40  8 

5 

40.9 

*, 

41.7 

/| 

t     Bootis           .                 \  9H*  " 

(04.  72) 

(5) 

(04.7) 

(5) 





4-  41  50  09.02 

8 

09.0 

g 

/?    Bootis  

4-  40  r>4  44.  85 

24 

45.  I 

10 

45.2 

7 

44.1 

7 

—    8  53  38.79 

40 

38  3 

1° 

39.7 

1-> 

38.3 

8 

38.7 

8 

fj.1   Bootis  

+  37  50  29.36 

34 

29  2 

10 

29.8 

11 

29.4 

7 

28.8 

6 

y3  Urese  Minoris  -  .  ......  .. 

+  72  18  13.48 

22 

14  8 

fi 

13.4 

^ 

13  6 

fi 

11.7 

•1 

y3  Ursae  Minoris,  S.  P  

12.2 

3 

a    CoroHse  Borealis  .-..  

+  27  09  37.  30 

46 

37  5 

14 

36  9 

11 

37.9 

q 

37.1 

q 

B.A.  C.  5157  

+  43  36  20.97 

7 

21  0 

7 

0    Bootis  .......       

4-  40  47  04.51 

7 

04.5 

7 

y    Coronse  Borealis    

4-  26  42  54.  00 

5 

54  0 

5 

a    Serpentis  

+    6  50  33  37 

43 

33  5 

1"> 

33  5 

13 

32.2 

10 

33  1 

8 

e    Serpentia  

4-    4  52  36  73 

35 

36  5 

q 

36  8 

1° 

36  9 

g 

36  8 

fi 

£    Ursse  Minoris  ........  ..... 

4-  78  11  57  04 

27 

57  8 

8 

56  9 

5 

56.3 

5 

56  4 

i\ 

f    Ursae  Minoris,  S.  P.  ..  --  

57.3 

5 

e    Coronas  Borealis  

+  27  15  41  54 

4 

41.5 

4 

(j     Scorpii  .            

—  22  14  37  14 

20 

37  9 

6 

37  1 

q 

36.2 

3 

36  4 

0 

B.  A.  C.  5313  

4-  55  07  25  31 

B 

25.3 

8 

/31  Scorpii         ...... 

—  19  26  30  28 

32 

31  2 

10 

2r<.  9 

11 

30.7 

fi 

30  9 

5 

Groombridge  2320  

+  66  09  29  24 

3 

29.2 

S 

tJ    Ophiuchi    ... 

—    3  21  08  86 

36 

08  9 

10 

08.5 

T> 

08.9 

q 

09.5 

fi 

16  Herculis          ....... 

4-  19  08  35  21 

7 

35  2 

7 

+  46  37  44  02 

33 

44  1 

10 

44  4 

10 

43.8 

fi 

43  6 

7 

4-  32  38  33  47 

7 

33  5 

7 

—  26  08  11  36 

32 

11  5 

10 

11  0 

10 

11  8 

8 

11.0 

4 

+  61  48  48  77 

14 

49  0 

8 

48  5 

fi 

4-  69  03  12  81 

17 

13  6 

4 

12  4 

12  5 

fi 

13.3 

a 

—  10  17  50  81 

30 

50  7 

10 

50  9 

10 

50.7 

fi 

51.2 

4 

4-  39  10  28  74 

29 

28  8 

10 

29  5 

11 

27.5 

fi 

28  1 

o 

K    Ophiuchi  

4-     9  34  56.06 

37 

55.8 

10 

57.0 

11 

55.7 

q 

55.5 

7 

J    Herculis 

-(-  33  45  39  36 

9 

39  0 

7 

40  5 

<> 

4-  82  14  59  46 

36 

59  6 

11 

59  3 

10 

59.3 

8 

59  2 

S 

e    Ursa^  Minoris,  S.  P. 

59.9 

4 

[Goj  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          471 

Wn  68 Catalogue — Continued. 


A   1  ..  |  ;  -  0 

_/ 

18» 

186 

r. 

186S 

i. 

186 

}. 

,! 

7T' 

i 

•K1 

f! 

IT1 

<i 

•K1 

BAG.  5801           

O        /           II 

+  55  56  11.70 

5 

n 

n 
11.7 

5 

it 

n 

+  14  32  34.23 

38 

34.1 

13 

33.8 

i^ 

34.6 

q 

35  0 

4 

+  37  25  52.74 

7 

52.7 

7 

B  A  C.5874           

+  40  06  21.28 

5 

21.3 

5 

—  24  03  03.  52 

30 

03.9 

10 

03.6 

10 

03.7 

7 

01  5 

3 

+  48  2-2  19.83 

7 

19.8 

7 

4-  52  23  59  44 

4 

59  4 

4 

+  12  39  29.50 

41 

28.8 

13 

29.6 

14 

30.4 

q 

29.4 

5 

+  68  49  07.42 

23 

07.0 

8 

07.8 

8 

07.6 

7 

-f-  27  47  58.50 

38 

58.5 

13 

58.3 

19. 

58.8 

7 

58.7 

6 

+  72  12  45.74 

15 

46.0 

q 

45.3 

6 

+  48  25  51.  15 

8 

51.1 

a 

+  51  30  19.41 

27 

19.1 

8 

19.4 

10 

19.7 

q 

—  30  25  21.  12 

9 

20.9 

5 

21.2 

4 

—  21  05  25.  63 

26 

26.3 

7 

2o.  0 

7 

26.0 

q 

24.7 

3 

+  86  36  18.64 

90 

18.8 

14 

19.1 

14 

18.5 

V> 

18.9 

4 

18.2 

14 

18.7 

13 

18.6 

q 

18  5 

10 

—    2  55  50.64 

18 

51.4 

7 

50.  1 

6 

50.3 

*> 

—    8  20  01.  75 

30 

01.5 

10 

01.8 

9 

01.9 

9 

02.1 

9 

+  38  39  44.05 

49 

44.4 

15 

43.9 

14 

43.6 

11 

44.2 

q 

110  Herculis 

+  20  25  18.77 

7 

18.8 

7 

+  33  12  39.  G3 

34 

39.6 

11 

39.9 

10 

39.3 

7 

39.5 

6 

—  26  27  27.  97 

go 

27.8 

7 

28.0 

8 

28.1 

7 

f>{)  Draconis  

-f  75  16  36.67 

27 

30.  3 

8 

36.6 

H 

37.4 

5 

50  Draconis,  S.P  

36.5 

5 

36.9 

1 

£     AquilsB  -.         ...... 

+  13  40  09.  68 

31 

09.7 

9 

09.8 

11 

10.0 

q 

07.7 

9 

+  32  17  42  44 

7 

42.4 

7 

+  65  45  27.60 

8 

27.7 

a 

d    Sagittarii. 

—  19  11  06.82 

7 

06.8 

7 

+  67  25  45.74 

23 

45.2 

7 

46.0 

9 

45.  3 

5 

47.7 

f 

T    Draconis    .... 

+  73  06  34.66 

11 

34.5 

5 

35.4 

4 

r    Draconis  SP 

33.6 

9 

+    2  51  13.44 

28 

13.7 

8 

13.5 

13 

13.1 

7 

4-  34  10  25.39 

7 

25.4 

7 

—    7  19  07.38 

29 

07.2 

9 

07.2 

10 

07.7 

10 

BAG  6748                      * 

_|_  54  40  54  77 

7 

54  8 

7 

4-  10  17  36.26 

41 

36.2 

11 

36.3 

13 

37.0 

10 

35.2 

7 

+    831  17.  88 

42 

18.1 

13 

17.5 

13 

18.7 

11 

16.4 

5 

4-  69  55  53.81 

14 

54.  1 

8 

53.4 

6 

(3    Aquilse  

+    6  04  44.04 

32 

44.4 

9 

44.2 

12 

43.8 

9 

42.6 

2 

+  88  54  44.93 

72 

44.6 

11 

45.1 

13 

44.9 

11 

45.2 

8 

44.9 

7 

44.8 

11 

45.1 

11 

-f    6  54  26.  07 

25 

26.0 

9 

26.6 

a 

25.6 

a 

—  12  57  06.64 

33 

06.9 

V? 

06.7 

11 

06.3 

10 

4-  77  18  44.85 

25 

45.2 

5 

44.8 

7 

K    Cepliei  S  P 

44.9 

7 

44.6 

3 

44.5 

3 

—  18  38  82.68 

28 

32.9 

9 

32.1 

10 

33.2 

9 

40  Cygni 

4-  38  00  28.51 

8 

28.5 

a 

+  36  00  55.  14 

7 

55.1 

7 

4-  10  51  22.68 

28 

22.3 

8 

23.3 

11 

22.3 

9 

ft    Cveni  ..                                ... 

-f  44  48  34.  59 

35 

34.9 

Is? 

34.9 

10 

34.0 

9 

34.4 

4 

—    9  28  36.  60 

27 

36.4 

8 

37.1 

q 

36.3 

10 

v    ^yj?1** 

-f  40  39  35.75 

30 

35.  4 

11 

36.4 

19 

35.2 

7 

GUCvirni 

4-  38  06  05.91 

30 

05.  8 

11 

06.  2 

19 

05.6 

7 

C    CvffQi 

4-  21)  41  11.90 

38 

11.9 

11 

12.2 

19 

11.7 

9 

11.5 

6 

472  UNITED  STATES  NOBTHEEN  BOUNDARY  COMMISSION.  [C6J 

Wn  68 Catalogue — Continued. 


*  i  ORO  n 

_/ 

186 

6. 

186 

7. 

186 

S. 

186 

9. 

6 

TT' 

(5 

*•' 

& 

•n' 

<! 

TT' 

a    Cephoi  

o    /      // 
+  62  01  36.  47 

35 

n 
36.5 

11 

n 
37.0 

11 

a 
34.9 

7 

n 
37  2 

6 

1    Pegasi  

+  19  14  27.54 

27 

27.8 

8 

27.3 

11 

27  5 

8 

0    Aquarii  

—    6  09  01.83 

33 

02.0 

10 

01.4 

1° 

02.  2 

6 

02  0 

5 

3    Cophei  

-f-  69  58  53.06 

22 

53.7 

8 

53.6 

7 

53.5 

4 

53  9 

3 

72  Cygni  

+  37  56  35.  91 

7 

35.9 

7 

f    Aquarii  

—    8  26  41.59 

22 

41.9 

7 

41.  1 

7 

41.8 

8 

e    Pegasi  

+     9  16  15.44 

41 

15.6 

10 

15.6 

n 

15  1 

q 

15  3 

9 

11  Cephei  

+  70  42  14.27 

20 

14.4 

8 

14.1 

7 

14.3 

!-, 

ft    Capricorn!....  

—  14  10  19.  12 

27 

19.1 

8 

18.4 

1° 

20.3 

7 

79  Draconis  

+  73  04  40.  94 

25 

41.2 

8 

40  2 

8 

79  Draconis,S.P  

42.2 

5 

40.4 

•i 

40  3 

1 

a    Aquarii  

—    0  57  36.  59 

26 

36.9 

11 

35.8 

11 

37.0 

q 

36  8 

5 

8    Aqnarii  

—    8  26  23.  01 

30 

23.2 

10 

22.5 

1° 

23.5 

8 

;r    Aquarii  

+    0  42  30.  17 

28 

30.6 

q 

30.2 

T> 

29.6 

7 

38  Pegasi  

-f  31  53  51.  40 

6 

51.4 

6 

a    Lacertos  

-f  49  36  15.38 

3 

15.  4 

•3 

TI    Aqnarii  

—    0  47  50.03 

30 

49.9 

11 

49.7 

10 

50.7 

7 

50.2 

2 

Cephei  (226  13)  

+  75  32  47.  16 

7 

47.1 

fi 

Cephei.  (226  B),  S.  P  

47.3 

1 

C    Pejrasi  .  . 

-f  10  08  34  33 

29 

34  0 

10 

34  o 

10 

35  3 

7 

34  1 

2 

£     Cephei    .. 

-(-  65  30  24  08 

17 

23  6 

8 

24  1 

3 

24  6 

6 

\    Aquarii  ........ 

—    8  16  53  20 

24 

53  6 

7 

52  5 

g 

53  5 

9 

d    Piscia  Australia   . 

—  30  19  16  74 

21 

16  8 

7 

16  2 

7 

17  2 

7 

a    Pegasi  ...... 

-f-  14  29  43  51 

43 

43  7 

12 

43  4 

13 

43  1 

9 

44  0 

9 

3    Andromedse  

+  49  20  05.40 

7 

05.2 

4 

05.6 

3 

o    Cephei  

+  07  23  22.58 

18 

23.0 

q 

22.2 

q 

8    Piscium  

+    5  39  14.32 

28 

13.9 

q 

14  6 

10 

14.5 

q 

i     Piscium  ... 

—    4  54  39  27 

30 

39  2 

q 

39  6 

10 

38  5 

9 

41  4 

2 

y    Cephei  

-f  76  53  44.  68 

32 

45.3 

q 

44.8 

44.5 

^ 

7    Cephei,  S.P  

41.9 

0 

44.8 

8 

44.2 

3 

Groombridge  4163.  

-f  73  40  32.42 

7 

32  4 

7 

o    Piscium  

+    6  07  56.46 

30 

56.8 

q 

56.1 

1'J 

56.6 

q 

The  value  of  "  C"  in  "Details  of  Corrections,"  etc.,  is  computed  from  these  declina- 
tions ;  and  in  column  "  obs."  the  values  of  d  are  given  instead  of  the  number  of  obser- 
vations. 

A  comparison  of  this  catalogue  with  the  polar  distances  of  the  Melbourne  General 
Catalogue  (Me  68)  may  not  be  devoid  of  interest.  The  mean  epochs  of  observation 
in  each  are  nearly  identical,  so  that  erroneous  proper  motions  will  be  practically  with- 
out influence  in  the  comparison.  In  the  comparison*  by  E.  J.  Stone,  of  Greenwich  and 
Melbourne  (to  which  reference  is  elsewhere  made),  the  refraction  at  the  latter  place 
Is  supposed  to  be  different  for  equal  zenith  distances  north  and  south.  From  circum- 
polar  stars  observed  at  Melbourne,  with  a  correction  of  +  "-15  to  y,  it  was  found  that 
the  adopted  refractions  should  be  multiplied  by  .99628.  From  comparisons  of  stars 
common  to  Greenwich  and  Melbourne  the  latter  quantity  was  found  to  be  .99086. 
These  resnlta  were  adopted  in  formation  of  Me  (i8.  Though  possible  ou  a  priori 
grounds,  this  hypothesis  is  open  to  serious  objections,  when  we  consider  the  difficulty 

•  E.  J.  Stone,  Month.  Not.,  28,  p.  27 


[67] 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          473 


of  determining  ( 1—  k)  independently,  at  the  latitude  of  Melbourne,  and  the  small  weight 
of  the  actual  determination,  with  a  circle  which  was  throughout  used  in  a  single 
position.  Before  comparing  I  have,  therefore,  reduced  the  polar  distances  of  Me  08 
to  those  which  would  have  resulted  from  circumpolar  stars  alone.  This  I  have  accom- 
plished by  the  application  of  the  correction  —  .00542  p  to  all  polar  distances  less  than 
127°  50'.  The  individual  weights  are  so  uniform  that  to  each  comparison  I  have 
assigned  weight  1,  these  excepted, —  a  Aurigse,  a  Cygni,  S  Scorpii,  a  Sagittarii,  and 
a  Columbae,  which  received  weight  0.5  j  and  a  Persei  and  i  Urs®  Majoris,  which  were 
rejected  for  obvious  reasons. 

If  p  be  the  computed  and  (1  —  Ic)  p  the  required  mean  refractions  at  Washington  for 
a  given  star,  p1  and  (1  —  fc')  />',  the  corresponding  quantities  for  the  same  star  at  Mel- 
bourne, and  if  —  M  =  P  (Wu)  —  P(Me),  we  shall  have  from  each  comparison  (n),  n' 
being  the  weight : 

\P  +  72.")  &  +  (/>'  +  75.")  k'  +  n  =  0}V-' 

The  two  catalogues  furnish  87  such  equations  which,  though  separately  formed, 
are  combined  for  convenience  of  solution  in  the  following  groups : 

Residuals  after 
substitution. 


65  k 

-f  538  k' 

72 

314 

79 

234 

83 

205 

90 

175 

95 

159 

100 

148 

105 

138 

109 

132 

117 

122 

124 

115 

136 

107 

151 

100 

165 

95 

176 

91 

191 

88 

219 

84 

260 

79 

3.  31  =  0 

1 

-1.06 

.96 

3 

+    .51 

.73 

4 

+    .49 

1.01 

6 

+    .12 

1.02 

9 

+    .03 

1.60 

5 

-    .58 

1.21 

8 

-    .21 

1.15 

6 

-    .16 

.98 

8 

+    .01 

.80 

7 

+    .18 

1.05 

6 

-    .05 

.87 

6 

+    .15 

1.13 

5 

-    .06 

.72 

2 

+    .40 

1.00 

2.5 

+    .15 

1.29 

3.5 

-    .08 

1.47 

0 

-    .14 

1.79 

0.5 

-    .29 

The  solution  gives 
Probable  error  (when 


k  =  +  .00468  ±  .00061 
Jc'  =  +  .00362  ±  .00045 
'  =  1)  =  ±  ".41 


The  refractions  at  Melbourne  are  already  (as  assumed),  Bessel's  (Tab.  Beg.)  x 
.99628.  They  now  become  0.99628  x  (1  —  .00362),  or  .99267  x  (Bessel's).  Those  at 
Washington  become  .99532  x  (Bessel's).  Admitting  that  e,  for  Melbourne  is  only  ±  .20, 
the  probable  error  of  an  average  single  P,  (wher>  rJ  =  1)  for  Me  68  is  roughly  ±  ".37. 


474          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[68] 


Judging  from  this,  the  hypothesis  adopted  to  explain  the  differences  Wn  68  —  Me  08 
is  uot  repugnant,  to  the  facts,  especially  when  we  bear  in  mind  that  the  Melbourne 
circle  has  remained  in  an  invariable  position  during  the  period  for  which  the  com- 
parison holdy  good.  But,  on  the  other  hand,  this  very  circumstance  throws  a  doubt 
upon  the  whole  discussion ;  for  we  can  form  but  an  imperfect  idea  of  the  degree  to  which 
our  work  may  be  affected  by  errors  in  adopted  division  and  flexure  correction,  and  by 
uncorrected  flexure,  such  as  has  been  suspected  in  the  Cape  circle.  (Month.  Not.,  vol. 
33,  p.  69.) 

I  have  formed  the  following  table  of— 

Corrections  to  polar  distances  of  Wn  68  and  Me  68. 


P. 

Wn  63. 

Me  68. 

P 

Wn  68. 

Me  68. 

I. 

II. 

III. 

IV. 

I. 

.11. 

III. 

IV. 

0 

0 

r> 

10 
15 
20 
25 
30 
35 
40 
45 
50 
55 
60 
65 
70 
75 
80 
85 
90 

// 

00 
—  .06 
—  .10 
—  .14 
—  .17 
—  .21 
—  .23 
—  .26 
—  .29 
—  .31 
—  .33 
—  .36 
—  .38 
—  .40 
—  .43 
—  .46 
—  .49 
—  .51 
—  .56 

// 

00 
—  .02 
—  .05 
—  .10 
-  .15 
—  .20 
—  .26 
—  .32 
36 

// 

/; 

o 
90 
95 
100 
105 
110 
115 
120 
125 
130 
135 
140 
145 
ICO 
lf.5 
100 
1(>5 
170 
175 
180 

// 

—  .56 
—  .60 
—  .65 
-  .71 
—  .79 
—  .89 
—  1.  04 
—  1.27 

// 

—  .59 
—  .59 
—  .60 
—  .63 
—  .70 
—  .80 
—  .93 
—  1.09 

// 

+  .19 
+  .*0 
+  .22 
+  .23 
+  .24 
+  .25 
+  .27 
+  .27 
+  .26 
+  .25 
+  .23 
+  .21 
+  .19 
+  .16 
+  -14 
+  -11 
+  .Od 
+  .04 
.00 

// 

+  .16 
+  .18 
+  .21 
+  .20 
+  .30 
+  .32 
+  .36 
+  .38 
+  .40 

+  .34 
+  .22 
+  .12 

+  .  05 
.00 

—  .39 
—  .42 
—  .45 
—  .47 
—  .50 
—  .53 
—  .55 
—  .57 
-  .58 
—  .59 

—  .20 
—  .06 

+  .02 
+  .07 

+  -11 
+  .lit 
+  .16 
+  .17 
+  .19 

—  .67 
—  .48 
—  .11 
+  .08 
+  .15 
+  .15 
+  .15 
+  .15 
+  .16 

Column  I.  exhibits  the  results  of  the  correction  (/>  +  72")  X  —  .00468  for  Wn  68. 
Column  II.,  for  purposes  of  comparison,  gives  the  final  correction  of  Wn  68  to  Normal 
System.  Column  III.  shows  the  correction  just  established  for  Me  68  by  comparison 
with  Washington.  For  stars  of  north  polar  distance  less  than  127°  50',  this  correction 
is  ".27  — .0018/>;  for  the  remainder  it  is,  (p+  75")  x  .00362.  These  corrections  are 
applicable  to  the  results  as  printed  in  the  ''General  Catalogue."  Column  IV.  gives 
the  adopted  correction  of  Me  684:o  Normal  System.  The  agreement  between  1.  and  II., 
as  well  as  between  III.  and  IV.,  is  such  as  to  strengthen  the  beliuf  that  a  great  part 
of  the  difference  Wn  68  —  Me  68  is  due  to  error  in  the  adopted  refractions  at  each 
observatory. 

Wn  72.  The  mean  corrections  to  polar  distance  of  American  Ephemeris,  or  simply 
polar  distance,  with  the  correction  for  "Div.  Flex.,  etc.,"  are  taken  as  printed  from  sec- 
tions entitled  "  Corrections  to  the  Star  Positions  of  the  American  Ephemeris,"  etc.,  and 
"  Mean  Places  of  Miscellaneous  Stars,"  etc.,  without  change  for  stars  of  polar  distance 
less  than  46°.  From  polar  distance  56°  southward  certain  corrections,  which  are  in- 


[GO] 


REPOET  OF  THE  CHIEF  ASTEONOMEB,  APPENDIX  H.  475 


eluded  in  the  reductions  on  account  of  discordance  between  direct  and  reflected  obser- 
vations, are  rejected.  The  effect  of  this  is  to  apply  the  following  corrections  to  polar 
distances,  or  what  is  the  same  thing,  to  the  correction  for  "Div.  Flex,  etc.,"  before 
adding  the  latter  to  the  polar  distance: — 


Year. 

Correction. 

1870 

// 
+  .31 

1871-2 

00 

1873 

-   .42 

1874 

—  .82 

Between  the  limits  56°  and  40°  (P.  D.)  these  corrections  are  interpolated  so  as  to 
become  zero  at  the  northern  limit.  By  some  accident  the  correction  — ".82  for  1874 
was  neglected  for  stars  between  polar  distances  102°  and  125°.  The  effect  of  this 
has  been,  quite  insignificant,  however,  since  the  preliminary  systematic  corrections 
depend  chiefly  on  residuals  of  stars  whose  polar  distance  is  less  than  102°. 

Proper  motion  has  not  been  applied  in  the  reductions  of  "  Miscellaneous  Stars." 
These,  I  have  corrected  accordingly. 

As  the  results  of  separate  years  so  taken  exhibit  considerable  systematic  discord- 
ances, for  use  in  the  discussion  of  systematic  corrections  I  have  pursued  a  course 
entirely  analogous  to  that  explained  under  Ee  66  and  72.  Following  is  a  list  of  correc- 
tions to  assumed  places,  thus  resulting : — 


// 

—  .19 
—  .43 
—  .68 
—  .41 
—  .46 

+  .02 
—  .32 
—1.14 
—  .35 

—  .54 

+1.60 
—  .34 
+  .18 
—  .17 
—  .34 

—  .12 
+1.49 
+  .12 
—1.04 
—  .04 

—  .30 
—  .45 
—  .56 
—  .12 

+  .57 

J3    Tauri 

// 

—  .26 
+  .20 
.21 

n 

—  .61 
+1.00 
—  .20 
—  .17 
—  .31 

+2.08 
—  .27 
—  .24 
+  .53 
—  .49 

—  .91 
—  .50 
+1.  :!8 
—  .CO 
.55 

d     Oriouis  

a.    Ursoe  Majoris  

3    Ceti 

+  .21 

—  .52 

—  .12 
+1.23 
—  .41 
—  .51 
—  .41 

—1.11 
—  .85 
+  .04 
—  .25 
—1.10 

.72 

J    Crateris  

T     Loon  is  .  .  

a    Ursaa  Minoris  
0    Ceti 

7}    Geiuiuorum.  ...... 

v    Leonis  

a    Geminorum.  ...... 

/3    Leonis  

y    Genrinorum  
e     Can  is  Majoris  

(j     Canis  Majoris  

y    Ursa}  Majoris  
o    Virginis  

ri    Virginis  

(j    Corvi  .. 

f     Ceti 

/5    Gcminorum.  ...... 

K    Draconis  

v     Ceti 

0    Geininorum  

a    CanamVen..  

0    Virginis  

+  .13 
—  1.25 
—  .17 
—  .67 

+  .09 

—  .74 
—  .50 
+  1.35 
+  .27 
—  .67 

i     Ursse  Majoris  
a*  Ureae  Majoris  

+  .40 

+  1.84 
.Ti 

f    Virgiuis  

77    Tauri 

rj    Ursa)  Majoris  
7j    Boot  is  .  

e    Tauri 

a    Hydras  

+  .41 

+  .49 

50 

a    Draconis  

E    Leonis  

n    Bootis  

+  .18 
—  .94 
—  .16 

5     Ursa?  Miuoris  
e     Bootis  r-- 

a2  Libras  

476 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[70J 


(3    Urase  Minoris      ... 

n 
-f  .34 

y2  Sagittarii  

// 
—  .51 

(3    Cephei 

n 
-4-     53 

8    Bootis  

-1-  .13 

M1   Sagittaiii.  ..  ...... 

—  .68 

4-    21 

(3    Librae  

—  .34 

<5    UrsiS  Minoris  ..... 

-1-  .28 

—  1  05 

ft    Bootis  ............ 

—  .67 

T]    Serpentis  -  --. 

—  .58 

4-  .32 

77 

4-    29 

81 

(i    Coronas  Borealis  .. 

—  .19 

8    Lyras  .  .  , 

—  .33 

7]    Acjuarii  ...... 

4-  .07 

—  .21 

—  .58 

4-  .18 

—    76 

—    02 

4-    27 

—    43 

3  82 

81 

—    22 

4-    19 

28 

—  .18 

+  .31 

a    Pesrasi.. 

—  .28 

—    22 

—1  81 

4-1  33 

—    51 

4-  .09 

4-1  17 

—    34 

4-    55 

—    57 

Q    Aquilaa  .              ... 

.92 

—  1  01 

a2  Capricorn! 

—    11 

K    Ophiuchi 

•4-    23 

4-1.57 

a    Herculis.       .  ... 

-t-  .81 

1.55 

44  Ophiuchi 

—  .72 

4-    44 

j3    Draconis  .         .... 

4-  .86 

1  19 

a    Ophiuchi  

-|-  .34 

4-  -11 

-1-  .73 

61  Cygni 

4-     80 

u    Herculis  ..         .   . 

—  .04 

£    Cveni 

—    45 

tpl  Draconis  ... 

—  .46 

4-     10 

v    Draconis  

—  .08 

B    Aquarii 

-1-  .13 

Discussion  of  3669  residuals  of  stars  most  frequently  observed  in  the  years  187 1-'73 
gives  for  the  probable  error  of  pointing : — 

e=  V  .4554  ( ±  .0122)  +  .0415  ( ±  .0076)  tan2  Z. 
The  values  tabulated  according  to  zenith  distance  are  these : — 


Z 

£ 

It, 

e 

Z 

c 

o 

// 

o 

n 

o 

/t 

0 

.675 

40 

.696 

60 

.762 

10 

.676 

45 

.705 

65 

.804 

20 

.679 

50 

.717 

70 

.877 

30 

.685 

55 

.735 

75 

1.02 

In  the  final  reductions,  separate  systematic  corrections  have  been  deduced  for  each 
year.  These  are  shown  in  Table  IX.  With  these  corrections  and  the  following  system 
of  weights,  the  definitive  values  of  €„  (vide  "  Details  of  Corrections  to  Assumed  Dec- 
linations") have  been  computed : — 

Weights  for  combination  of  Wn  70-74. 


Number  of 
observations. 

Weight. 

Number  of 
observations. 

Weight. 

1 

1 

8  to  11 

5 

2 

2 

12  to  16 

6 

3 

2.5 

17  to  27 

7 

4 

3 

28  to  51 

8 

5  to  7 

4 

52,  or  more 

9 

[71]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          477 

SECTION  VI. 

FIRST  APPROXIMATION  TO  NORMAL  SYSTEM. 

It  will  be  assumed  that  the  catalogues  to  be  used  in  tbe  formation  of  the  Normal 
System  have  received  all  the  corrections  which  can  be  applied  solely  on  the  authority 
of  the  observations  composing  each  of  them.  It  will  also  be  taken  for  granted  that  the 
correction  furnished  by  a  given  catalogue  to  the  assumed  declination  is  of  the  form: — 

rpi         m 

A  8  +  A  ,j.i  — £, 

100    ' 

where  A  5  is  the  correction  of  S  for  a  given  epoch,  T  (T1  being  the  mean  epoch  of  each 

•  A  u! 
catalogue),  and  ~£,  the  correction  to  the  assumed  annual  variation.    This  course  is 

only  proper  when  the  path  of  proper  motion  does  not  deviate  sensibly  from  the  arc  of 
a  great  circle.  That  there  is  such  deviation  in  the  cases  of  Sirius  and  Procyon  has 
been  pretty  well  established  by  Dr.  Auwers  and  others;  but  these  stars  are  omitted  in 
our  catalogue.  It  is  possible  that  variable  proper  motion  may  ultimately  be  found  in 
the  large  majority  of  cases,  but,  a  few  binary  systems  excepted,  the  evidence  of  such 
variability  at  present  appears  to  be  wanting. 

If  now  no  discrepancies  of  a  constan  t  character  were  found  to  exist  between  the 
determinations  of  different  observatories,  nothing  further  would  remain  except  to  deter- 
mine the  relative  weights,  and  by  means  of  conditional  equations,  derive  a  correction 
for  each  assumed  declination.  On  the  other  hand,  granting  the  existence  of  these  dif- 
ferences, we  should  be  justified  in  adopting  the  samecour&e,  if  the  declination  of  every 
star  in  a  given  catalogue  were  made  with  equal  weight,  and  if  each  of  the  stars  under 
consideration  had  been  determined  in  each  of  the  authorities.  This,  however,  is  by  no 
means  the  case,  and  in  order  to  prevent  the  undue  influence  of  large  systematic  errors 
in  case  of  stars  for  whose  declinations  there  are  few  authorities,  it  remains  to  be  ascer- 
tained what  corrections  of  a  constant  and  periodic  character  can  be  applied  to  each 
catalogue.  This  can  be  accomplished  by  means  of  comparison  with  standard  declina- 
tions, which  are  free  from  any  such  error. 

From  the  nature  of  the  case  this  standard  can  never  be  attained.  The  best  that 
can  be  done  is  to  consider  the  combined  testimony  of  all  independent  determinations 
available  for  the  purpose.  To  take  any  two  determinations  as  standard,  to  the  exclu- 
sion of  all  others,  would  be  manifestly  an  error,  for  it  would  be  assuming  that  the  weight 
of  these  selected  catalogues  in  comparison  with  the  remainder  is  as  infinity  to  zero, 
while  all  experience  teaches  that  the  best  independent  determinations  of  declination 
are  subject  to  comparatively  large  errors. 

There  is,  however,  great  difference  in  the  quality  of  these  so-called  independent 
determinations,  which  vary  from  such  special  investigations  as  those  of  Kg  21,  Dt  24, 
Ao  30,  and  Pa  45,  where  every  precaution  has  been  exercised  to  remedy  the  inevitable 
defects  of  instruments  by  variety  in  the  circumstances  of  observation,  and  the  utmost 
skill  and  rigor  in  the  computations,  with  determination  of  the  various  elements  of  atmos- 
pheric refraction, — to  those  which  assume  their  refractions  from  alien  authority,  which 
are  made  with  non-reversible  instruments,  and  with  little  attention  to  those  details  of  ob- 
servation and  reduction  so  essential  in  the  delicate  problem  of  measuring  absolute  decli- 
nation. It  seems  but  reasonable  to  suppose  that  declinations  of  the  former  class  are 


478          UNITED  STATES  NOETHEBN  BOUNDABY  COMMISSION. 


entitled  to  much  greater  confidence  tban  those  of  the  latter.    This  I  have  endeavored 
to  express  through  the  following  system  of  weights  to  be  employed  in  the  preliminary 

discussion : — 

Weights. 


Authority. 

Weight. 

Authority. 

Weight. 

Authority. 

Weight. 

Kg  21 
Gh22 

4 
1 

Kg  43 
Eh  43 

2 
1 

Gh  57 
CGH58 

2 
1 

Dt24 

5 

Gh45 

2 

Wn64 

1 

Ao29 

5 

Pa  45 

10 

Gh64 

2 

Sh31 

1 

Ee45 

1 

Ln67 

8 

CGH33 

a 

Wn47 

I 

Me  68 

2 

Ce34 

i 

Ce48 

1 

Wn68 

3 

Eh  37 

i 

Gh51 

1 

Re  68 

2 

Kg  38 

2 

Ps  53 

3 

Gh?0 

2 

GU39 

2 

So  55 

1 

Wn72 

1 

Ce40 

1 

Wn56 

1 

For  the  purpose  proposed  in  this  section,  weight  zero  was  assigned  to  all  other 
catalogues.  A  few  are  excluded  on  the  ground  that,  although  independent,  their 
weight  is  so  small  that  they  would  merely  encumber  the  computation  with  useless 
material. 

These  weights  are  not  those  which  might  seem  to  be  required  by  comparisons  with 
an  approximate  mean  system,  but  are  derived  from  an  independent  study  of  each  cat- 
alogue, considered  solely  on  the  basis  of  internal  evidence,  with  the  assistance  of  such 
critical  reviews  as  have  been  found  conveniently  accessible. 

They  result  from  careful  study,  but  are  necessarily  arbitrary,  and  can  only  bo 
regarded  as  mere  expressions  of  opinion  concerning  the  relative  contribution  made  by 
each  determination  to  the  problem  of  finding  an  absolute  system  of  declinations.  It 
would  therefore  be  superfluous,  and  at  all  events  a  tedious  task  to  mention  in  detail 
the  facts  and  arguments  relied  upon  in  support  of  each  individual  weight. 

It  will  be  sufficient  to  notice  some  of  the  principles  adopted,  which  are  of  general 
application  and  tolerably  definite  and  well  established. 

An  investigation,  founded  on  a  series  of  observations  for  declination,  will  be 
regarded  as  independent,  or  absolute,  in  proportion  to  its  freedom  from  any  assumption 
whatever  founded  upon  results  from  other  series  of  observations,  having  in  view  the 
same  or  any  other  purpose.  Practically,  however,  the  determination  of  aberration, 
nutation,  and  precession  can  be  left  to  special  investigations.  On  the  other  hand,  it 
may  be  doubted  whether  the  constant  of  refraction  or  of  atmospheric  expansion  is 
sensibly  the  same  for  different  regions  and  climates ;  even  if  it  were,  in  practical  influ- 
ence on  observations,  much  would  still  depend  upon  local  conditions  and  upon  the 
character  and  situation  of  the  meteorological  instruments.  Add  to  this  the  uncertainty 
of  any  existing  single  determination,  and  it  will  hardly  be  maintained  that  any  series  of 
declination  observations  is  strictly  independent,  which  does  not  include  the  determina- 
tion of  refraction  constant  and  coefficient  of  expansion  for  atmospheric  air,  by  proper 
methods  and  adequate  means,  from  the  observations  themselves. 

Every  series  of  observations  professing  to  give  independent  declinations  should 
contain  satisfactory  evidence  as  to  the  character  and  amount  of  its  instrumental  cor- 
rections. In  this  connection  the  excellence  of  the  mechanical  construction  of  the 


[73] 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          479 


instrument  becomes  an  important  consideration.  Thus  the  work  of  the  older  instru- 
ments labors  under  disadvantage.  It  is  plain  that  the  greater  the  variety  of  circum- 
stances under  which  an  instrument  may  be  used,  other  things  being  equal,  the  greater 
will  be  the  freedom  from  constant  errors  due  to  instrumental  causes.  Therefore,  results 
from  instruments  which  admit  of  reversal  have  received  the  preference  over  others. 
Furthermore,  when  the  relation  of  the  circle  to  the  telescope  is  so  altered  that  its  read- 
ings for  a  given  zenith  distance  vary  from  year  to  year,  this  has  been  regarded  as  a 
decided  advantage.  This  consideration  becomes  of  less  importance,  however,  with 
finely  graduated  instruments  read  by  a  large  number  of  microscopes.  The  real  advan- 
tage of  reflection  observations  is  supposed  to  be  an  open  question.  It  has  been  ably 
debated  by  Bessel,  Faye,  Dollen,  Airy,  Kaiser,  and  others.  In  cases  where  the  dis- 
cordance R  —  D  is  large,  and  not  accounted  for  by  special  investigations  of  the  instru- 
ment, this  circumstance  has  been  regarded  as  just  cause  for  suspicion. 

Where  we  have  a  long  series  of  observations  made  at  the  same  observatory,  or 
with  the  same  instrument,  the  weight  of  each  group  is  considerably  reduced  from  that 
which  would  have  been  assigned  to  it  when  standing  as  the  sole  representative  of  the 
particular  series. 

Thoroughness  and  skill  in  the  methods  of  reduction  were  allowed  to  have  an 
important  bearing  upon  the  decision  of  these  weights. 

Lastly,  the  degree  of  liability  to  fortuitous  errors  is  an  element  which  has  been 
considered.  With  the  older  catalogues  it  is  a  highly  important  one.  The  catalogue 
of  Piazzi,  for  instance,  is  essentially  independent,  but  its  chance  errors  are  such  that 
had  we  been  assured  of  its  entire  freedom  from  systematic  error,  it  would  still  have 
received  a  weight  practically  insignificant  by  comparison  with  the  determinations 
actually  used  in  the  present  discussion.  In  a  less  degree  the  same  is  true  of  Bradley's 
declinations  for  1755. 

These  weights  were  applied,  without  alteration,  to  all  the  declinations  of  the  respect- 
ive authorities,  where  the  star  was  observed  at  least  four  times  at  a  zenith  distance  of 
70°  or  less;  beyond  70°,  weights  were  diminished  by  the  use  of  empirical  factors, 
diminishing  nearly  in  proportion  to  the  reciprocal  of  the  square  of  the  refraction; 
being  zero  for  all  zenith  distances  greater  than  80°,  and  in  cases  where  the  weight 
multiplied  by  the  factor  is  less  than  .5. 

The  results  of  the  various  series  of  determinations  made  by  observatories  in  the 
southern  hemisphere,  were  never  used  beyond  70°  zenith  distance;  so  that  from  the 
pole  down  to  and  including  a  Virginis,  there  was  no  diminution  of  weights  for  this 
cause. 

The  factors  are  these : 


z 

Factor 

Z 

Factor. 

o 

// 

o 

// 

70 

1.0 

76 

.5 

71 

.9 

77 

.4 

72 

.8 

78 

.3 

73 

.7 

79 

.3 

74 

.6 

60 

.2 

75 

.6 

480 


UNITED  STATES  NOETHEEN  BOUNDAET  COMMISSION. 


[74] 


Two  or  three  observations  received  half-  weight;  a  single  observation,  weight  zero. 

Now  while  there  is  great  disparity  in  the  number  of  authorities  relating  to  differ- 
ent stars,  fortunately  a  considerable  number  of  stars  have  been  quite  universally 
observed.  They  are  known  as  the  fundamental  stars,  to  which  may  be  added  a  Persei, 
tj  Ursa?  Majoris,  f  Draconis,  /9  Draconis,  ?  Ursae  Majoris,  a  Cassiopesp,  a  Cephei,  a  Ursae 
Mnjoris,  /3  Cephei,  /?  Ursae  Minoris,  f  Cephei,  C  Ursae  Minoris,  <5  Ursae  Minoris,  and 
a  Ursae  Minoris.  Tb  ise  have  each  been  frequently  observed  in  a  majority  of  the  series 
of  observations  enumerated  above  (Class  I).  It  will  be  possible,  therefore,  in  the  case 
of  these  stars,  without  the  intervention  of  systematic  corrections,  to  compute  declina- 
tions which  shall  be  measurably  free  from  error,  and  thus  answer  the  purpose  of  an 
approximate  normal  system,  to  be  subsequently  revised  and  improved. 

The  results  of  this  preliminary  discussion  are  exhibited  in  Table  I.  The  first 
column  contains  the  name  of  the  star  ;  the  second  and  third,  respectively,  values  of 
[J  d]  and  [J  fi']  determined  in  the  following  manner.  For  each  catalogue  an  equation 
of  condition  was  constructed  of  the  form  : 

„,  -0  =  0 


The  values  of  0  are  those  given  in  column  G  of  Table  A,  "  Details  of  Corrections  to 
Assumed  Declinations."  The  epoch  1845  is  selected  to  facilitate  the  solution  of  the 
equations.  T'  is  the  designation  for  mean  epoch  and  is  sufficiently  indicated  in  the 
numerical  part  of  the  designation  of  the  catalogues  concerned.  These  values  of  [  J  d] 
and  [J  //]  are  those  which  result  from  the  use  of  Gh  1755,  without  final  correction  and 
•with  weight  1.  The  fourth  and  fifth  columns  contain  A  d  and  J/i',  with  Bradley's 
declinations  excluded;  and  these  values  are  used  in  forming  the  preliminary  system 
of  corrections.  The  sixth  and  seventh  columns  contain,  respectively,  the  probable 
errors  of  the  adopted  J  S  and  A  /*'.  The  eighth  contains  the  probable  error  of  the  unit 
of  weight.  The  last  column  contains  the  approximate  declination  for  1845. 

TABLE  I. 


Name  of  star. 

[A«J] 

CV] 

M 

bpf 

eM 

v 

£ 

d 

(i    Virginis 

// 
+    045 

II 

—    848 

a 
+    052 

it 
1  003 

a 
055 

// 
345 

ii 
.47 

o 
—10.4 

P    OrioDis   ... 

+     193 

—  .  100 

+  .187 

—    014 

.062 

.390 

.53 

—  8.4 

a    HydraB  .... 

4-     111 

—  .430 

+  .  128 

784 

.062 

.387 

.52 

—  8.0 

a    Aqnarii  ......  . 

—  .022 

—  .148 

—  .009 

—    405 

.071 

441 

.60 

—  1.1 

—  .  178 

—  .106 

—  .207 

+    487 

.035 

.340 

.46 

4-3.5 

—  .149 

—  .493 

—  .136 

—    740 

.055 

345 

.47 

4-6.0 

a    Serpentis  .  ......  .... 

—  .002 

+  .023 

4-  .028 

—    569 

,059 

.366 

.50 

4-6.9 

-4-  .022 

—    075 

4-  .019 

—    0°0 

.056 

.349 

.47 

4-7.4 

a    A  ({  i  ii  ]  ;  n  

+  .022 

+  .248 

4-  .040 

—  .  104 

051 

.319 

.43 

4-8.5 

y    Aqnilse  

—  .005 

—  .102 

+  .003 

—    251 

.056 

.348 

.46 

4-10.2 

+    032 

694 

+    056 

1  177 

062 

385 

52 

4-12  7 

a    Ophiuchi  

+     105 

—    217 

4-     111 

1  046 

003 

394 

53 

4-12  7 

y    Pe^asi  .  , 

—    228 

—    22(5 

231 

164 

061 

373 

51 

4-14  3 

«    Pegasi  .  ......  ...... 

4-    285 

—    914 

+     330 

1  8°5 

038 

268 

38 

4-14  4 

+  .173 

4-     141 

-\-     197 

336 

060 

372 

51 

+14  6 

4-    229 

•    1  844 

+    259 

•    °  141 

047 

288 

39 

+15  4 

a    Tauri  .  ... 

+    032 

219 

4-    060 

790 

067 

415 

56 

+16  2 

[75|  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 

TABLE  I — Continued. 


481 


Name  of  star. 

[AtS] 

CV] 

A<! 

«f 

£A<! 

V 

£• 

6 

a    Bootis  .     ....  ...... 

// 

—  .265 

It 

—1.378 

// 
—  .234 

// 
—2.  020 

// 

.048 

II 

.297 

// 

.40 

a 
+20.0 

a    Arietis    ..   -...  ... 

—  .138 

—  .459 

—  .128 

—  .649 

.047 

.293 

.40 

+22.  7 

a    Coronje  Borealis  
a    Andromedaj  

—  .067 
—  .164 

—  .016 
—  .420 

—  .018 
—  .144 

—  .996 

—  .904 

.052 
.056 

.345 
.377 

.43 

.46 

+27.  2 
+28.  2 

{3    Gemiuornm  

—  .220 

—  .  164 

—  .206 

—  .430 

.041 

.254 

.34 

+28.  4 

(3    Tauri  

-  .i?7 

—  .182 

—  .247 

+  .349 

.047 

.292 

.39 

+28.5 

a    Lyrae  

a    Cvfrni  .. 

+  .345 
+  .0-27 

—1.  258 

—  .800 

+  .362 
+  .031 

—1.627 

—  .880 

.044 
.049 

.273 
.309 

.36 
.40 

+38.6 
+44.7 

—  .006 

—  .241 

+  .010 

—  .579 

.063 

.393 

.51 

+45.8 

—  .2-23 

+  .098 

lisas 

+  .333 

.063 

.396 

.50 

+49.3 

+  .090 

—  .899 

+  .098 

—1.013 

.045 

.276 

.35 

+50.1 

—  .031 

—  .058 

-.051 

+  .347 

.059 

.361 

.46 

+51.5 

+  .134 

+  .343 

+  .129 

+  .411 

.067 

.428 

.47 

+52.  4 

+  .192 

—  .164 

+  .196 

—  .251 

.049 

.301 

.SH 

+54.  6 

+  .024 

—  .452 

+  .023 

-  .428 

.059 

.366 

.46 

+55.7 

—  .024 

+  .321 

—  .067 

+1.  682 

.057 

.355 

.45 

+61.9 

+  .042 

—  .775 

+  .025 

—  .454 

.053 

.327 

.41 

+62.  6 

+  .060 

—  .088 

—  .014 

+1.  326 

.038 

.233 

.29 

+69.9 

—  .009 

—  .099 

—  .070 

+1.  050 

.043 

.263 

.33 

+74.8 

4-  .041 

+1.  196 

+  .045 

+1.122 

.045 

.279 

.35 

+76.8 

—  .146 

—  .071 

-  .  127 

—  .393 

.041 

.247 

.31 

+78.3 

+  .009 

+  .659 

.06 

.20 

+86.6 

+  .087 

—  .258 

.03 

.10 

+88.5 

—  .314 

+  .593 

.072 

.449 

.61 

—13.  0 

+  .063 

—2.  133 

.084 

.524 

.71 

—15.4 

—  .020 

+  .353 

.086 

.541 

.45 

—26.1 

—  .505 

—  .380 

.126 

.782 

.49 

—30.4 

The  weights  assigned  in  the  case  of  the  two  polar  stars  a  and  8  Ursse  Minoris,  are 
not  those  of  the  table,  since  the  relative  weights  here  depend  on  principles  entirely 
different  from  those  which  have  governed  in  the  selections  of  weights  to  be  used  with 
equatorial  stars.  The  weights  are  those  given  in  column  -  of  the  tables  for  these  two 
stars. 

The  four  stars  a2  Capriconi,  a2  Libra,  a  Scorpii  and  aPiscis  Australis  are  not  found 
in  "table  A,"  since  the  subsequent  process  with  these  is  exactly  the  same  as  for  other 
stars  iu  the  same  region. 

The  formation  of  normal  places  for  the  limits  —  30°  to  —  90°  decimation  is  re- 
served for  a  later  period  of  the  discussion,  and  the  manner  will  be  hereafter  explained. 

By  the  substitution  in  the  equations  of  condition  of  the  values  of  A  8  and  A  //  con- 
tained iu  columns  four  and  five,  we  derive  the  numbers  in  column  "r",  table  A, 
"Details  of  Corrections,"  etc.  These  are  the  corrections  to  the  catalogue  declinations 
given  by  the  approximate  Normal  System.  These  are  arranged  for  each  catalogue  in 
the  order  of  declination,  and  from  them  systematic  corrections  derived,  which  are 
exhibited  in  Table  IJ 
N  B 31 


482          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[76] 


TABLK  II. 

Preliminary  systematic  corrections  to  fundamental  catalogues,  derived  through  comparison 
with  the  declinations  of  forty -four  fundamental  and  circumpolar  stars. 


i 

53 
tf 

a 
9 

3 

gi 

S.H.31.* 

3 

d 

0 

if 

o 

s 

If 

9 

ri 

S 

® 
0 

8 

i 

•j 

a 

jj 

i 

i 

00 

" 

" 

+    05 

00 

.40 

J-2. 

-.40 

00 

00 

-30 

00 

--    07 

00 

.40 

-2.00 

+1    Ji 

-.40 

00 

00 

-28 

00 

40 

00 

+1  90 

+1.54 

—.40 

00 

00 

-Ofi 

00 

+    11 

00 

40 

00 

-1.85 

--1.  33 

.40 

00 

00 

00 

—24 

00 

1  10 

--    13 

00 

—.40 

00 

-1.80 

+1.17 

-.40 

00 

00 

00 

+.71 

-22 

-20 

+.25 

00 

-  .94 

-1.22 

--  .15 

00 

-.40 

00 

+1.65 

--1.04 

-.40 

00 

00 

00 

+.51 

+.68 

-20 

-18 
-16 

+.25 
+.25 

03 
00 

-  .82 
-  .72 

-1.03 
-  .90 

--  .17 
--  .19 

00 
00 

-.40 
-.40 

oo 

00 

+1.  50 
+1.38 

--  .93 

-  -  .  85 

-.40 
-.40 

00 
00 

00 

00 

00 

+.04 

+.50 
+.50 

+.65 
+.01 

-18 
-16 

-14 
-13 

+  24 
+.24 

00 
00 

-  .65 
-  .59 

-  .80 
-  .72 

+1.21 
+1.23 

00 
00 

-.40 
-.40 

00 
00 

+1.26 
+1.18 

+  .76 
+  .70 

-.40 
-.40 

00 
00 

+.10 

+.22 

+.08 
+.12 

+.50 
+.49 

+.58 
+.56 

-14 
-12 

-10 

+  24 

00 

-  .54 

-  .65 

+  .94 

+.25 

—.40 

+.07 

+1.10 

+  .65 

-.40 

00 

+.40 

+.16 

+.49 

+.54 

-10 

-  8 
-  6 

+.24 
+.24 

00 
00 

-  .51 
—  .47 

-  .60 
-  .55 

--  .97 
--  .00 

+.20 
+  16 

-.41 
-.42 

+.06 
+.05 

+1.04 
+  .98 

+  .60 
+  .55 

-.41 
-.42 

--.02 
--.05 

-.39 
-.39 

+.16 
+.16 

-.49 
-.48 

+.51 
+.48 

-  8 
-  6 

-  5 

-  93 

00 

-  .45 

-  .53 

--  .02 

+.16 

-.42 

+.04 

-  .92 

+  .53 

-.42 

--.06 

-.38 

+.16 

-.48 

--.46 

-  5 

—  4 

-.23 

00 

-  .44 

-  .51 

--  .07 

+.15 

-.43 

+.04 

-  .P8 

+  .51 

-.43 

--.07 

-.38 

-i.  16 

-.48 

-  -.  42 

-  4 

-  2 

-.23 

00 

-  .41 

-  .48 

--  .09 

+.15 

-.44 

+.03 

-  .81 

+  .48 

-.44 

--.09 

-.37 

+.16 

-.47 

--.33 

-  2 

0 

-  23 

00 

-  .39 

-  .45 

--  .12 

+.09 

-.45 

+.  02 

-  .74 

+  .44 

-.45 

--.10 

-.37 

+.16 

-.47 

--.24 

0 

--  2 

-.23 

00 

-  .37 

-  .42 

--  .16 

+.03 

-.46 

+.01 

-  .68 

+  -41 

-.46 

--.11 

-.35 

+.17 

-.46 

--.14 

- 

-  2 

--  4 

-  99 

00 

-  .35 

-  .40 

--  .17 

-.02 

-.48 

00 

-  .62 

+  .39 

-.48 

--.12 

-.33 

+.18 

-.46 

--.05 

- 

-  4 

--  5 

-  99. 

00 

—  .34 

-  .39 

--  .18 

-.08 

-.49 

-.00 

-  .58 

+  .37 

-.49 

--.13 

-.32 

+.18 

-.45 

00 

- 

-  5 

--  6 

-.22 

00 

-  .33 

-  .38 

--1.19 

-.13 

-.50 

-.01 

-  .55 

+  .36 

-.50 

--.14 

-.31 

+.18 

-.44 

-.04 

- 

-  6 

+  8 
+10 

+.21 
+.21 

00 
00 

-  .32 
-  .30 

-  .36 
—  .34 

--1.21 
-  -1.  24 

-.21 
-.30 

-.52 
-.53 

-.02 
-.03 

--  .47 
-  .43 

+  .34 
+  .31 

-.52 
-.53 

--.15 
--.16 

+.29 
+.27 

+.19 
+.20 

-.44 
-.43 

—.12 
-.20 

+  8 
+10 

+15 

+.19 

00 

-  .27 

-  .31 

+1.31 

-.31 

-.58 

-.06 

+  .28 

+  .28 

-.61 

+.18 

+.20 

+.21 

+.41 

-.34 

+15 

(-20 
+25 
+30 

k!8 
-.17 
-.16 

00 
00 
00 

-  .24 
-  .22 
-  .20 

-  .28 
-  .25 
-  .22 

+1.44 
+1.53 
+1.52 

-.08 
+.12 
+.05 

-.63 
-.70 
-.75 

-.09 
-.11 
-.14 

+  !os 

--  .07 

+  .22 
+  .18 
4-.H 

-.70 
-.78 
-.(ft 

--.20 
--.21 
--.23 

+.14 
+.  07 
00 

+.22 

4%  17 
+.12 

-.39 
-.37 
-.34 

-.47 
-.56 
-.CO 

+20 
+25 
-|-30 

--35 

-  14 

00 

-  .18 

-  .20 

+1.34 

-.20 

-.75 

—.17 

--  .14 

+  .11 

-.80 

--.24 

-.  05 

+.05 

-.31 

-.50 

- 

-;to 

--40 

-.13 

00 

-  .16 

-  .18 

-  -1.  12 

-.60 

-.70 

-.20 

--  .22 

+  .07 

-.78 

--.26 

-.10 

-.02 

-.29 

-.28 

-40 

--45 

+.12 

-  .14 

-  .16 

-  -1.  02 

-.61 

-.22 

--  .28 

+  .04 

-.66 

--.27 

-.13 

-.06 

-.26 

-.10 

. 

-45 

--50 

1.  11 

-  .13 

-  .15 

--  .94 



-.53 

-.25 

--  .28 

+  .01 

-.54 

--.29 

-.10 

-.10 

-.23 

+.02 

. 

-50 

--55 

+.06 

-  .11 

—  .13 

--  .98 



-.41 

-.27 

--  .19 

00 

-.45 

+.30 

-.05 

-.05 

-.20 

--.08 

* 

-55 

--60 

00 

-  .10 

-  .11 

-  -1.  07 

-.30 

-.30 

--  .10 

00 

-.27 

00 

00 

-.17 

--.12 

. 

-60 

00 

-  .08 

-  .09 

-  -1.  21 



-.24 

-.27 

00 

00 

-.13 

...... 

00 

00 

-.14 

--.23 

- 

-6b 

-  -70 

00 

07 

08 

18 

25 

10 

00 

00 

00 

00 

-.11 

--.58 

-7(1 

--75 

00 

-  .05 

-  .06 

-.13 

-.19 

-  .05 

00 

00 

00 

00 

-.08 

+.76 

+75 

--80 

00 

-  .04 

-  .04 

-.09 

-.13 

00 

00 

CO 

00 

00 

-.05 

--.fiO 

+80 

+90 

00 

00 

00 

00 

00 

00 

00 

00 

00 

•   •   • 

00 

00 

00 

+90 

The  correction  to  S.  H.  31  is  applicable  to  the  declinations  as  printed  in  the  catalogue. 


NOTE. — These  corrections  are  applicable,  of  course,  to  the  catalogues  as  affected  by  the  preliminary 
corrections  explained  in  Section  V. 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


483 


TABLK  II — Continued. 


i 

I 

5 

* 

$ 

S 

d 

4 

to 
m 

o 

B 
d 

Si 

s 

5 

8 

s 

Q 

oo 

to 

s 

H 

» 

£ 

• 

a 

$ 

& 

4 

1 

J3 

O 

d 

£ 

o 

3 

s 

a 

£ 

o 

& 

M 

C5 

is 

o 
-30 

00 

+.72 

+.28 

00 

-.so 

-.24 

-.27 

+  1.04 

00 

-30 

-28 

-.05 

"66' 

'"60 

+.50 

+  .28 

-.05 

+.":i6 

-.20 

-.'.4 

""66 

"66" 

-.26 

•"-  .97 

-.25 

-i.'io 

CO 

-as 

-26 

-.10 

00 

00 

+.S9 

+.28 

-.10 

+.^0 

-.10 

-.£4 

00 

00 

-.26 

(-  .92 

-.25 

-1.37 

00 

-26 

-24 

-.15 

00 

00 

+.15 

+.28 

-.15 

+  .30 

-.•JO 

.14 

00 

00 

-.25 

+  .87 

-.25 

-1.34 

00 

-24 

-22 

-.20 

00 

00 

+.02 

+.28 

—.20 

f.SO 

-.20 

—.24 

oo 

00 

-.24 

+  .83 

-.25 

-1.31 

00 

-22 

-SO 

-.25 

00 

00 

-.03 

+.28 

—  .  25 

+  .30 

-.20 

-.\!4 

00 

00 

-.24 

+  .79 

-.25 

-1.S8 

00 

-£0 

-18 

-.30 

oo 

00 

-.09 

+.28 

-.20 

+  .30 

-.to 

-.24 

00 

00 

-.23 

+  .75 

-.25 

-1.24 

oo 

-18 

-10 

-.35 

00 

00 

-.17 

+.28 

-.35 

+.30 

-.29 

—.24 

00 

00 

-.23 

+  .72 

-.25 

-1.21 

00 

-16 

-14 

-.40 

00 

00 

—.24 

+.29 

-.40 

+.30 

-.£0 

—  24 

-.06 

03 

-.22 

+  .70 

-.25 

-1.10 

00 

-14 

-I* 

-.43 

00 

00 

-.29 

+.28 

-.45 

+.30 

-.20 

-.44 

-.13 

00 

-.83 

+  .67 

-.25 

-1.12 

-.05 

-12 

-10 

-.50 

-.30 

+.05 

-.34 

+.28 

-.  r,o 

f.SO 

-.SO 

—.24 

-.18 

+.13 

-.22 

+  .65 

-.86 

-1.08 

-.10 

-10 

-  8 

-.49 

-.29 

+  .06 

-.32 

+.28 

-.53 

+.30 

-.5:0 

—  .  25 

-.14 

+.10 

-.21 

+  .63 

-.29 

-1.03 

-.10 

-  8 

-  0 

-.48 

+.08 

-.30 

+.28 

-.50 

+.30 

-.so 

-.25 

-.11 

+.07 

-.20 

+  .61 

-.32 

-  .98 

-.10 

—  « 

-  5 

-.47 

-!iJ7 

+.08 

—  .  S9 

+.28 

-.40 

+.30 

-.so 

-.25 

-.09 

+.05 

-.20 

+  .60 

-.34 

-  .96 

-.10 

-  5 

4 

-.47 

-.87 

+.00 

-.28 

+.C8 

-.49 

+  .30 

-.20 

-.26 

-.07 

+.04 

-.20 

+  .59 

-.36 

-  .94 

-.10 

-  4 

-  2 

-.46 

-.26 

+.11 

-.26 

+-2< 

-.47 

+.30 

-.£0 

-.i6 

-.04 

+.01 

-.20 

+  .57 

-.39 

-  .69 

-.10 

a 

0 

-.45 

-.25 

4..  12 

-.24 

+.28 

-.46 

+.30 

-.£0 

-.27 

00 

-.02 

-.19 

+  .56 

-.42 

-  .84 

-.10 

0 

+  2 

-.44 

-.25 

+.14 

-.22 

+.28 

-.45 

+.30 

-.20 

-.28 

+.03 

-.05 

-.18 

+  .54 

-.44 

-  .80 

-.11 

+  a 

+  4 

-.4-2 

-.25 

+  .16 

-.20 

+.28 

-.43 

+.30 

-.19 

-.28 

+.06 

-.08 

-.18 

+  .53 

-.46 

-  .75 

-.13 

+  4 

+  5 

—.41 

-.25 

+.17 

-.19 

+.18 

-.42 

+.30 

-.19 

-.28 

+.08 

-.10 

-.17 

+  .52 

-.46 

-  .73 

-.13 

+  5 

+  6 

-.41 

-.25 

+.17 

-.18 

+.Z8 

-.41 

+.30 

-.19 

-.29 

+.10 

-.12 

-.17 

4-  .51 

-.46 

-  .71 

-.14 

+  6 

+  8 

-.39 

-.25 

+.18 

-.16 

+  .28 

-.39 

+.30 

-.  17 

-.29 

+.13 

-.  15 

-.16 

+  .50 

-.48 

-  .66 

-.16 

+  8 

+10 

-.38 

-.25 

+.18 

-.14 

+.23 

-.38 

+.30 

-.15 

-.30 

+.16 

-.18 

-.16 

+  .49 

-.50 

-  .62 

-.17 

+  10 

15 

-.34 

-.34 

+.17 

-.09 

+.28 

-.34 

+.30 

-.10 

-.29 

+.18 

-.26 

-.13 

+  .46 

-.50 

-  .53 

-.18 

15 

20 

-.30 

-.40 

+.10 

-.04 

+  .28 

-.30 

+.30 

-.00 

-.26 

+.20 

-.29 

-.11 

+  .43 

-.46 

-  .45 

-.20 

20 

85 

-.26 

-.50 

+.01 

+.01 

+  .28 

-.25 

+.3'l 

-.<>9 

—.21 

+.17 

-.30 

-.07 

+  .40 

-.37 

-  .38 

-.20 

25 

30 

-.22 

-.60 

-.03 

+.06 

+  .28 

-.21 

+.30 

-.12 

-.16 

+.14 

-.30 

-.0-i 

+  .38 

-.26 

-  .34 

-.20 

30 

35 

-.18 

-.65 

-.11 

+.11 

+.28 

-.17 

+.30 

-.22 

-.08 

+.09 

-.30 

+.06 

+  .36 

—.15 

-  .31 

-.20 

:<5 

40 

-  14 

-.70 

—.15 

+.16 

+.28 

-.13 

+.30 

00 

+.04 

-.30 

+.20 

+  .33 

-.04 

-  .29 

-.20 

40 

45 

-.10 

-.66 

-.14 

+.22 

-.07 

+.29 

00 

00 

-.30 

+  .31 

+.06 

-  .28 

-.20 

45 

50 

-.06 

-.62 

—.13 

+.28 

.. 

-.02 

+.28 

00 

00 

-.28 

.... 

+  .29 

+  .13 

-  .28 

-.20 

50 

55 

-.01 

-.51 

—.11 

+.30 



+.07 

+.26 

00 

00 

-.25 

.... 

+  .26 

+.17 

-  .28 

-.18 

55 

60 

+.04 

-.40 

-.10 

+.33 

+.17 

+.25 

00 

00 

-.21 

. 

+  .23 

+.21 

-  .SB 

-.17 

60 

65 

+.12 

-.27 

-.08 

+.31 

+  .S6 

+.23 

00 

00 

-.16 

+  .21 

+.22 

-  .26 

-.13 

65 

•;o 

+.20 

-.15 

-.06 

+  .30 

+.29 

+.22 

00 

00 

-.10 

+  .17 

+.18 

-  .25 

-.10 

70 

75 

+.26 

-.07 

-.04 

+.22 



+.28 

+.16 

00 

00 

00 

+  .14 

+.09 

-  .20 

-.05 

75 

80 

+  .25 

00 

-.03 

+.15 

+  .26 

+.11 

00 

oo 

00 

+  .10 

00 

-  .16 

00 

80 

99 

+.10 

00 

00 

00 

+.20 

90 

00 

00 

00 

'    ' 

+  00 

00 

00 

00 

90 

*  The  correction  actually  used  by  mistake  for  Co  48  between  the  limits  of  —  13°  and  —  30°  was  +  ".13. 
t  As  actually  naed,  the  correction  from  —  13°  to  —  30°  was  about  —  ".20.    See  explanation  (p.  69). 

The  following  explanations  will  servo  to  show  the  manner  of  computing  these 
corrections.  As  the  points  of  comparison  were  relatively  few,  sudden  fluctuations  in 
the  values  of  the  correction  are  to  be  avoided,  unless  they  seem  to  be  completely 
justified  by  the  testimony  of  the  observations.  Whenever  a  general  expression  such 
as  a  (sin  Z  +  sin  Z'),  or,  a  (tan  Z  +  tan  Z'),  (where  Z'  is  the  zenith  distance  of  the 
pole),  was  found  to  represent,  approximately,  the  residuals,  r,  it  was  adopted.  In  the 
derivation  of  the  corrections  from  —10°  to  +90°  declination,  only  stars  within  those 
limits  were  used.  From  —10°  to  —34°,  the  corrections  are  very  rough  approxima- 
tions, there  being  but  four  standard  declinations  within  these  limits  to  control  the 
curves.  In  fact,  the  curves  were  continued,  in  many  cases,  according  to  the  law 
adopted  for  them  within  the  limits  +90°  to  —10°,  where  this  course  was  not  too 
strongly  opposed  to  the  residuals  given  by  the  four  southern  stars.* 

We  proceed  to  notice  such  peculiarities  in  the  individual  corrections  as  appear  to 
bo  worthy  of  remark. 

*  The  methods  nted  in  deducing  some  of  the  corrections  of  Table  II.  are  not  entirely  satisfactory  to 
the  writer,  but  were  rendered  practically  unavoidable  for  reasons  which  are  given  in  the  introductory. 
(Seep.  [4].) 


484 


UNITED  STATES  SOUTHERN  BOUNDARY  COMMISSION. 


178] 


Kg  21.  I  have  supposed  that  the  systematic  error  in  this  catalogue  is  more  likely 
to  be  due  to  error  in  the  constant  of  flexure  employed  than  to  anything  else.  This  is 
found  to  correspond  well  with  the  residuals.  Assuming  the  correction  to  be  of  the 
form,  a  (sin  Z+  sin  Z'),  we  have  for  a  +  ".16,  The  use  of  this  formula  was  continued 
to  the  extreme  southern  limit. 

Gh  22.  The  correction  is  so  small  and  so  uncertain,  that  zero  has  been  adopted  for 
all  declinations. 


Dt  24.  The  correction  is  assumed  to  be  of  the  form  * 


. 


where  p  and  p'  are 


respectively  the  mean  refractions  for  a  given  star  and  the  pole.    We  have  : 

x  =  -  .299 

The  Dorpat  observations  are  reduced  with  a  refraction  constant  which  is  Bessel's 
multiplied  by  .99545.*  Prom  the  formula  we  shall  have  as  the  true  factor,  .99545  X 
1.00299  =  .99843.  The  following  table  shows  the  agreement  of  the  formula  with  the 
means  of  the  several  groups  of  residuals. 


Mean  <J  of 
group. 

Number 
of  stars. 

Mean  value 
of  r. 

Formula. 

Residual. 

o 

it 

H 

// 

—    8.9 

3 

—  .49 

—  .53 

—  .04 

H-    5.2 

6 

—  .53 

—  .34 

+  .19 

+  13.8 

8 

—  .21 

—  .27 

-.06 

+  25.8 

6 

—  .03 

—  .22 

—  .19 

+  43.0 

3 

—  .17 

—  .  15 

+  .02 

+  52.3 

5 

—  .25 

—  .13 

+  .12 

+  62.3 

2 

—  .18 

—  .10 

+  .08 

+  75.0 

4 

—  .08 

—  .06 

+  .02 

Ao  29.  The  process  with  this  correction  was  exactly  similar  to  that  pursued  with 
Dt24.    We  have:— 

x  =  -  .333 
and  the  following  comparison : — 


Mean  6  of 
group. 

Number 
ofstars. 

Mean  value 
ofr. 

Formula. 

Residual. 

o 

It 

// 

it 

—    8.9 

3 

—  .58 

—  .62 

-  .04 

-t-    5.2 

6 

—  .34 

—  .39 

-  .05 

+  13.8 

8 

—  .36 

—  .:;2 

+  .04 

+  25.8 

6 

—  .33 

—  .25 

+  .08 

+  43.0 

3 

—  .28 

—  .17 

+  .11 

+  52.3 

6 

—  .03 

—  .14 

—  .11 

+  62.3 

2 

—  .02 

—  .10 

—  .07 

+  75.0 

4 

+  .06 

—  .06 

—  .11 

8.  H.  31.  From  decimation  +60°  to  —10°,  the  curve  was  formed  by  adding  to  the 
numbers  given  by  Dr.  Auwers  for  S.  H.  31  (Ast.  Nach.  Bd.  64,  8.  378),  the  difference 

*  Pos,  Med.  (Struve),  p.  xxxii,  Int. 


[79] 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


485 


between  the  correction  just  deduced  for  Ao  29  and  that  given  by  Dr.  Auwers  (ibid.),  tho 
difference  being  taken  in  the  sense  Normal  —  Auwers.  For  the  limits  —10°  to  —30°, 
the  catalogue  places  corrected  to  Bessel's  refraction,  were  taken  without  change. 

C.  G.  H.  33.  The  correction  for  this  catalogue  was  formed  in  precisely  the  same 
manner  as  that  of  S.  H.  31,  and  between  the  limits  —10°  and  —30°,  correction  zero  is 
arbitrarily  adopted. 

Ce  34.  The  residuals  were  plotted  on  a  convenient  scale  as  ordinates,  both  singly 
and  in  groups,  with  the  mean  declinations  as  absciss*.  A  curve  of  the  simplest  form 
was  then  drawn  by  hand,  passing  as  nearly  as  possible  through  the  mean  of  the  points. 

Eh  37  and  Eh  43.  Constructed  on  similar  principles  to  that  of  Ce  34. 

Kg  38.  A  hand-curve  was  drawn,  but  was  found  to  be  very  uncertain. 

Gh  39.  In  the  interval  +  90°  to  +  52°,  the  correction  zero  was  assumed.  The 
remaining  interval  is  well  represented  by  the  formula,  —  ".61  tan  Z,  which  is  adopted. 

Ce  40  and  Ce  48.  Process  same  as  for  Ce  34. 

Kg  43.  The  formula  of  correction  assumed  is  :  — 


The  values  derived  are  these:  K=  +  ".30  ±  ".09;  *  =  —  .24  ±  .15.  The  correc- 
tion zero  is  assumed  between  the  limits  —  10°  and  —  30°,  though  from  the  formula  a 
small  minus  correction  would  result. 

Pa  45.  The  adopted  form  of  correction  is  a  (sin  Z  +  .503),  the  decimal  number  being 
the  approximate  sine  of  the  co-latitude.  This  would  closely  represent  the  effect  of  an 
error  in  the  adopted  coefficient  of  sine  flexure.  There  is  room  for  reasonable  doubt 
whether  the  constancy  of  the  coefficient  of  flexure  can  be  relied  upon  where  the  ocular 
and  objective  are  interchanged  as  at  Poulkova.  At  any  rate,  as  will  appear  from  the 
subjoined  table  of  comparison,  this  formula  accounts  very  accurately  for  the  difference, 
Normal  —  Ponlkova.  The  value  of  the  constant  is  +  ".341  ±  ".015:  — 


Mean  6  of 
group. 

Number  of 

stars. 

Mean  valno    Formi]la_ 

Residual. 

// 

II 

// 

—    8.9 

3 

+  .49        +  .49 

.00 

+    5.2 
+  13.8 

6 

8 

+  .43 

+  .48 

+  .45 
+  .42 

+  .03 
-  .06 

+  25.8 

6 

+  .31 

+  .36 

+  .05 

+  43.0 

3 

+  .25 

+  .27 

+  .02 

+  52.3 

6 

+  .16 

+  .21 

+  .05 

+  62.  3 

2 

+  .38 

+  .16 

—  .22 

+  75.0 

4 

—  .02 

+  .08 

+  .10 

The  use  of  this  formula  is  continued  to  the  southern  limit. 

Gh  45.  A  simple  hand-curve  is  drawn. 

Re  45.  Owing  to  the  large  probable  error  of  this  authority,  and  the  uncertainty  of 
the  curve,  a  comparison  with  Pa  45  and  Gh  45  is  instituted  for  every  star  in  common 
with  these  catalogues  and  that  at  the  end  of  this  paper.  The  comparisons  are  included 
within  the  limits  +90°  and  —10°  declination,  and  are  in  the  sense  of  corrections  to 


486 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[ST.] 


Re  45.  The  weights  were  adopted  without  reference  to  the  number  of  observations  in 
Pa  45  or  Gh  45,  unless  the  number  in  the  former  is  less  than  4  and  in  the  latter  less 
thau  5.  With  this  exception,  the  weights  are  these: — 


Observations 
iu  Re  45. 

Weight. 

1 

.4 

2 

.0 

3  or  4 

.8 

5  or  more 

1.0 

These  were  multiplied  by  .5  when  the  number  of  observations  iu  either  of  the  other 
catalogues  is  1,  by  .7  when  in  Gh  45  the  number  is  2,  by  .8  when  in  Pa  45  the  number 
is  either  2  or  3,  and  in  Gh  45,  3  or  4.  It  was  seldom  necessary  to  use  these  factors. 
The  following  table  contains  iu  the  first  column  the  meau  declinations  of  the  groups 
Pa — Re;  in  the  second,  the  mean  residual  Pa — Re  for  each  group;  iu  the  (bird,  the 
weight;  in  the  fourth,  the  probable  error  of  the  nuit  of  this  weight  determined  from 
each  group. 

The  fifth,  sixth,  and  seventh  columns  contain  corresponding  particulars  for  Gh  45 — 
Re  45,  omitting  the  probable  errors,  which  were  not  determined.  The  eighth  and  ninth 
columns  show  respectively  the  sums  of  numbers  in  columns  two  and  six  added  to  the 
corresponding  corrections  of  Pa  45  and  Gh  45,  taken  from  Table  II.  The  tenth  column 
contains  the  means  of  columns  eight  and  nine,  giving  the  numbers  iu  column  eight 
double  weight  except  for  the  first  group.  From  this  last  column  the  curve  of  correc- 
tion is  constructed  graphically  by  the  usual  method. 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

o 

// 

// 

o 

II 

// 

II 

II 

—  8.4 

-  .33 

6 

-j-  .GO 

—  8.6 

+  .40 

8 

+  .16 

+  .56 

+  .36 

—  0.8 

+  .15 

6 

.45 

—  1.3 

+  .53 

9 

+  .62 

+  .69 

+  .64 

+  3.5 

—  .78 

5 

.41 

+  3.6 

—  .60 

6 

—  .32 

—  .43 

—  .36 

+  8.1 

—  .66 

15 

.31 

+  8.0 

—  .18 

15 

—  .22 

00 

—  .15 

+  13.7 

—  .77 

9 

.43 

+  13.6 

—  .41 

10 

—  .36 

—  .20 

—  .31 

+  18.1 

—  .42 

6 

.46 

+  18.3 

—  .23 

6 

—  .02 

—  .01 

—  .02 

+  22.8 

—1.10 

9 

.48 

+  22.9 

—  .89 

9 

—  .72 

—  .70 

—  .71 

+  28.0 

—  .87 

7 

.40 

+  28.1 

—  .57 

6 

—  .52 

—  .43 

—  .49 

+  35.  1 

—1.34 

5 

.46 

+  35.1 

—  .81 

3 

—1.03 

—  .76 

—  .94 

+  41.1 

—  .68 

20 

.45 

+  41.4 

—  .03 

22 

—  .40 

—  .06 

—  .29 

+  47.2 

—  .34 

19 

.44 

+  47.2 

+  .22 

24 

—  .09 

+  -14 

—  .01 

+  52.0 

—  .24 

12 

.35 

+  51.8 

+  .12 

15 

—  .02 

+  .04 

00 

+  C6.8 

—  .07 

10 

.61 

+  56.7 

+  .15 

14 

+  .12 

+  -12 

+  .12 

+  01.  0 

—  .07 

13 

.21 

+  60.6 

+  .06 

21 

+  .09 

+  .06 

+  .08 

+  c:;.o 

+  .01 

6 

.13 

+  66.1 

+  .2o  ' 

9 

+  -14 

+  .26 

+  .18 

+  70.9 

+  .66 

11 

.32 

+  70.1 

+  .64 

10 

+  .76 

+  .06 

+  .73 

+  70.5 

+1.03 

7 

.33 

+  76.8 

+  .52 

9 

+1.12 

+  .52 

+  .92 

L85.  8] 

r—  .  121 

F85  71 

C-i-  321 

L      *•*-  J 

t"1"  *  j 

L  r  •  «f~j 

The  correction  of  the  table  is  not  considered  applicable  between  the  limits  80°  and 
90°  declination  when  stars  are  observed  both  above  and  below  the  pole.  Between 
the  limits  —  10°  and  —22°  the  curve  was  constructed  by  the  help  of  Dr.  Auwers's 
table  (Ast.  Nach.,  Bd.  64).  Search  for  terms  in  the  declination  correction  of  Re  45, 
which  depend  upon  the  right  ciscension  of  the  star  for  their  magnitude,  failed  to  dis- 


[81] 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


48' 


cover  any  which  it  was  thought  sale  to  apply.  Dr.  Gould  finds  a  considerable  cor- 
rection of  this  kind  (Ast.  Nach.,  Bd.  05,  s.  182),  and  Dr.  Auwers  (Ast.  NacJi.,  Bd.  64, 
s.  335)  finds  by  comparison  with  Ao  29:  +  ".285  sin  a  —  ".140  cos  a.  My  comparison 
includes  stars  between  —  10°  and  +  74°  declination,  and,  after  subtracting  (he  differ- 
ence of  declination  corrections  from  the  separate  differences  Pa  —  Re  and  Gh  —  Re,  I 
find :— 


Pa  45  —  Re  45. 

Gh  45  —  Re  45. 

Mean  a 
of  group. 

Weight. 

Difference. 

Mean  a 
of  group. 

Weight. 

Difference. 

Ji. 

// 

h. 

// 

0.2 

14 

—  .11 

0.1 

17 

—  .02 

2.2 

17 

+  .10 

2.2 

18 

+  .21 

4.2 

13 

+  .13 

4.2 

13 

+  .21 

5.8 

11 

—  .12 

5.8 

13 

—  .18 

8.1 

10 

+  .0» 

8.1 

11 

+  .06 

10.1 

15 

—  .38 

10.1 

14 

—  .52 

12.1 

8 

—  .01 

12.2 

14 

+  .01 

14.0 

11 

.00 

14.1 

14 

+  .37 

16.0 

15 

—  .30 

1C.O 

16 

—  .25 

18.0 

8 

—  .34 

18.0 

12 

+  .15 

19.9 

ir> 

+  .02 

19.9 

18 

+  .26 

22.0 

15 

—  .06 

22.0 

24 

4-  .20 

Wn  47,  Wn  56,  Wn  64.  The  corrections  were  derived  by  the  graphical  process. 
None  of  these  curves  are  very  certain  for  declinations  north  of  40°. 

Gh  51,  Gh  57,  and  Gh  64,  Ps  53,  C.  G.  H.  58,  Ln  67,  Re  68,  and  Wu  72  were  also 
discussed  by  means  of  hand  curves. 

So  55.  A  uniform  value  of  the  correction  was  adopted,  since  sufficient  material  for 
drawing  the  cu^ve  with  requisite  certainty  was  not  available. 

Me  68  and  Wn  68.  Comparison  with  the  residuals  r  shows  that  the  results  of  the 
discussion  of  Washington  and  Melbourne  declinations  (p.  68)  answer  sufficiently  well 
for  the  first  approximation  to  their  respective  corrections.  This  opinion  is  supported 
by  the  final  discussions. 

Gh  70.  The  empirical  formula  a  (sin3  Z+  sin3  Z'),  which  differs  little  in  practical 
effect  from  that  employed  with  Dt  24  and  Ao  -D,  though  it  does  not  very  closely  rep- 
resent the  mean  values  of  r,  is  adopted.  Discussion  of  the  separate  residuals  gives  for 
a  —  1".17.  The  comparison  with  means  is  as  follows : — 


Mean  f  of 
group. 

Number 
of  stars. 

Mean  r. 

Formula. 

0  —  0. 

o 

n 

// 

n 

—    8.9 

3 

—  1.12 

—  1.05 

+  .07 

4-    5.2 

6 

—    .74 

—    .73 

+  .01 

+  13.8 

8 

—    .33 

—    .55 

—  .22 

-j-  25.8 

6 

—    .35 

—    .39 

—  .04 

4-  43.0 

3 

—    .38 

—    .29 

4-  .09 

+  52.3 

6 

—    .50 

—    .28 

+  .22 

+  62.  3 

2 

—    .37 

—    .27 

+  .10 

+  75.  0 

4 

—    .46 

—    .£0 

+  .26 

488 


UNITED  STATES  NOKTHEKN  BOUNDAKY  COMMISSION. 


|8J] 


If,  for  instance,  observations  have  been  corrected  by  the  formula  a  sin  Z  cos2  Z, 
when  the  true  formula  is  a  sin  Z,  then  the  correction  «  sin3  Z  would  be  required  for  the 
polar  distances,  as  published.  The  average  correction  to  zenith  distances  by  direct 
observation  during  the  years  18G8-'72  for  R  —  D  is 

+  ".75  sin  Z  cos2  Z. 

If  we  suppose  that  this  correction  should  have  In-eu  approximately  +  ".75  sin  Z,  then 
declinations  would  require  the  correction  —".75  sin3  Z  +  (the  proper  correction  for  lat- 
itude). 

It  is,  however,  probable  that  a  great  part  of  the  correction  is  due  to  error  in  the 
adopted  constant  of  refraction. 

SECTION  VII. 

CORRECTION  OF  BESSEL'S  FUNDAMENTA  ASTRONOMLE. 

With  the  systematic  corrections  of  Table  II.,  and  with  the  system  of  weights 
already  used,  we  proceed  to  correct  the  assumed  declinations  of  stars  of  class  "i>"  (p. 
8).  The  object  of  this  is  to  secure  a  greater  number  of  points  with  which  to  compare 
Bradley's  declinations,  and  even  this  additional  number  is  insufficient  for  the  satisfac- 
tory solution  of  the  problem.  The  criterion  of  selection  of  these  additional  stars  is 
that  there  shall  be  none  for  which  the  weight  of  A /if  is  less  than  .5.  The  formation  and 
solution  of  conditional  equations  was  conducted  on  precisely  the  same  principles  as  for 
the  fundamental  stars.  The  same  authorities  were  used  (Gh  1752  and  1755  being  of 
course  excluded),  but  they  were  first  corrected  by  Table  II.  in  order  to  diminish  the 
effect  of  uneven  distribution  of  systematic  errors  in  the  series  of  corrections  for  a  given 
star. 

The  results  are  shown  in  Table  III.  where  the  adopted  corrections  of  fundamental 
and  circumpolar  stars  (Section  VI.)  are  repeated  for  convenience.  The  explanation 
follows : 

TABLE  III. 


17 

55. 

v  .. 

TA  ' 

Cor.  to 

a 

<! 

&/i' 

&ff 

Bradley. 

o 
319  6 

o 
+88  5 

it 
+    258 

it 
+1  18 

// 
1  \ 

// 
4.     1 

10.9 

+H8.  0 

+    Od7 

—    26 

—  1  9 

2  0 

4-     3 

<5    Ursoe  Miuoris  .... 

282.7 

+86.5 

+    009 

+    66 

4  1 

1  0 

—  2  3 

Camelop.  (32  H.)  .... 
e     UrsBB  Miuoris  .  

192.  0 
25H.  0 

+84.7 
+82.  4 

+  .569 

+  .  189 



+3.  83 
—    63 



—  .2 

—    0 

1.0 
4 

+  -7 

£    Ursie  Miuoris 

233  3 

+78  5 

127 

57  9 

39 

1  56 

1  ° 

1  0 

4-     fi 

y    Cephei  .   . 

352  4 

+76  3 

+     045 

01  4 

4-1    12 

1  60 

4-     5 

1  0 

_(_')  <> 

f>     Urea;  Miuoris  .  . 

217  1 

+76  » 

+     605 

27  0 

-4-4  07 

83 

32 

1  0 

1  '! 

/3    Ursse  Miuoris  ....... 

222  9 

+75  2 

+     0/0 

60  4 

+1  05 

1  59 

3  1 

4 

-2  0 

X    Druconis  

276  4 

4-72  6 

+     456 

26  3 

1  28 

£9 

4-1   :i 

1  0 

1  8 

ya  UrsiB  Miuoris  
ill1  Draconis  
^    Draconis  

230.3 
266.6 
169.  1 

+72.7 
+72.  :t 

+70  7 

—  .073 

+  .  Ob6 
+     456 

43.4 
15.  9 

40  0 

—1.57 
—  .30 

4-4  17 

1.18 

.54 
90 

+4.0 
7 

3*5 

1.0 
1.0 
1  0 

+3.8 
+1.0 
-    3  1 

321  4 

+69  5 

014 

61  0 

+1  3f 

1  60 

3  7 

1  0 

"  0 

<j    Draoonis 

264  6 

+6d  9 

402 

18  8 

4-2  90 

52 

3  6 

1  0 

1  2 

[83]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  489 

TABLE  III — Continued. 


Name  of  star. 

1755. 

AS 

if., 
M 

A/,' 

TA      / 
Aft' 

Cor.  to 
Bradley. 

w' 

Resdual. 

a 

6 

<73  UrsflB  Majoris  

0 

132.1 

288.1 
340.  3 
209.4 

o 
+68.1 
+67.2 
+64.9 
+65.  6 
+62.4 

+03.1 
+01.6 
+62.1 
+60.9 
+61.5 

+60.0 
+60.2 
+59.1 
+59.2 
+58.4 

+57.2 
+57.0 
+57.7 
+56.3 
+55.  2 

+56.2 
+55.  1 
+52.5 
+52.9 
+53.0 

+52.  5 
+52.8 
+51.  5 
+51.2 
+50.5 

+49.7 
+49.0 
+49.  0 
+49.0 
+49.  1 

+47.4 
+47.0 
+47.  2 
+45.  7 
+45.8 

+44.9 
+44.4 
+44.1 
+43.  4 
+43.  0 

+42.7 
+41.1 
+40.9 
+40.0 
+39.5 

II 

+  .778 
+  .076 
+  .072 
+  .242 
+  .201 

+  .025 
—  .067 
+  .203 
—  .  381 
+  .067 

—  .  154 
+  .328 
+  .154 
+  .019 
—  .242 

+  .009 
+  .227 
+  .444 
+  .175 
+  .023 

—  .004 
+  .196 
—  .  082 
—  .352 
—  .125 

+  .129 
—  .346 
—  .051 
—  .056 
+  .098 

—  .445 

+  .101 
—  .235 

—  .278 
+  .056 

—  .397 
—  .264 
—  .431 
+  .010 
—  .234 

—  .079 
+  .030 
—  .594 
+  .166 
—  .  142 

+  .304 
+  .262 
+  .242 
+  .461 
+  .428 

16.9 
47.5 
41.6 
48.2 
40.6 

61.4 
61.4 
49.2 
32.  8 
31.0 

29.0 
43.3 
21.2 

44.0 
37.2 

30.2 
41.3 
35.9 
16.0 
62.7 

42.0 
61.1 
27.7 
32.  6 
41.4 

50.3 
45.4 
00.2 
31.5 
61.3 

31.8 
27.3 
62.7 

44.8 
40.1 

29.6 
39.3 
27.8 
64.9 
32.1 

44.1 

66.1 
38.3 
32.  0 

28.1 

29.  4 
30.6 
37.4 
31).  8 
45.3 

it 

+4.46 
+  1.01 
+1.18 
+  .12 
—  .07 

—  .45 
+1.68 
—1.06 
+1.64 
+1.61 

+1.52 
—  .08 
+  .27 
+1.02 
+1.37 

+2.41 
—  .68 
—4.  25 
+  .>-2 
—  .43 

+  .53 

—  .25 
—  .24 

+  .87 
—  .90 

+  .41 
+  .94 
+  .35 
—  .02 
—1.01 

+1.85 
—  .73 
+  .33 
+  .06 
—  .68 

+  .60 
+  .33 
+1.03 
—  .58 
+  .52 

—  .08 
—  .88 
+1.77 
—1.59 
+  .06 

—1.69 
+  1.14 
—1.40 
—1.31 
—2.67 

.  52 
1.14 
.90 
.25 
.00 

.60 
.60 
.35 
.75 

.57 

.95 
1.05 
.68 
1.21 
.82 

.54 
.97 
.87 
.60 
1.63 

1.08 
1.59 
.70 
.78 
1.19 

1.23 
1.04 
1.00 
.74 
1.60 

.96 

.69 
1.63 

.85 
.97 

.70 
.97 
.59 
1.66 
.71 

1.06 
1.69 
.91 
.91 
.70 

.74 
.73 
1.05 
1.12 
1.14 

a 

—3.8 
—2.0 
—1.5 
—  .2 
—  .2 

—  .8 
—3.6 
—1.6 
—2.0 
—1.7 

—2.2 

—  .5 
—2.6 
—1.6 
—4.2 

—2.  5 
—2.3 
+4.0 
—1.8 
—  .1 

—  .4 
+  -2 
+  -9 
—1.2 

+  -7 

—  .1 
+  .2 
—1.1 

+  .4 
+  -3 

—2.5 

±:l 

—1.7 

—  .8 

—  1.5 
—  .5 
—  .7 
+  -9 
—  ?.4 

—  .7 
+  -2 
—1.6 

ft! 

+» 

+  -9 
+1.6 
+2.4 

.4 
1.0 
1.0 
1.0 
1.0 

1.0 
1.0 

.7 
1.0 
1.0 

1.0 
1.0 
0.4 
1.0 
1.0 

1.0 
1.0 
1.0 
1.0 

1.5 

1.5 
1.0 
1.0 
2.0 
1.0 

2.0 
1.0 
2.0 
2.0 
1.5 

.4 
1.0 
1.5 
1.0 
1.0 

1.0 
1.5 
.4 

2.r> 

.7 

2'.0 
1.0 
'1.0 
1.0 

1.0 
1.0 
1.0 
1.0 
1.5 

it 

—4.3 
—1.1 
0.0 
+  -2 
+  -7 

—  .6 
—2.3 
—1.7 
—  .5 

—  .8 

—  .6 
—  .3 

-1.5 
—  .8 
—2.6 

-  .8 
—  .8 
+1.9 

—  !9 

—  .2 
0.0 
+1.0 
—  .2 
+  -5 

+  -3 
—  .4 
—  .6 
+1.6 
+  .4 

—1.5 
+  -3 
—  .6 

—  .7 
+  -9 

—1.4 
—  .3 
—  .5 
+  1.1 
—1.6 

—  .6 
—  .5 
—1.0 
—1.3 
+1.0 

+1.5 

+  .'<3 
+  -9 
+  .9 

<J     Dr  aeon  is  .....  ...... 

(     Cepliei  .   

a    Draconis     

c     Cassiopeiaj  

24.3 

162.1 
318.2 
245.  2 
310.1 
122.4 

324.6 
143.  3 
281.  9 
239.  3 
97.2 

335.  0 
330.  6 
161.7 
66.9 
6.7 

198.5 
175.2 
5.9 
287.9 
214.2 

261.2 
139.1 
267.7 
290.9 
204.  5 

292.5 
335.3 
46.7 
130.  6. 
173.3 

20.8 
51.4 
211.8 
74.7 
103.  9 

85.4 
308.3 
150.6 
71.1 
246.  6 

151.  9 
27.2 
72.  3 
43.1 
303.4 

a    Ursro  Majoris  ......  .  . 

q    Draconis.  

v    Ursa?  Majoris  

f1    Ursse  Majoris  

Q    Urssts  Majoris 

i2    Cygni  

TJ    Ursse  Majoris  
e    Cvffni 

a    Lacertce  

%    Ursse  Majoris  
51  Atulroniedsd  

A    IJootis  

tb    Ursao  Majoris  ...... 

/?    Aurigas  

a     Cygni  

>l    IJrsaj  Majoris  

e     A  urigse  

<T    Herculis  ......  ...... 

ri    Anrigra  
ft    Pursei  

•y    Cv^ni    . 

490          UNITED  STATES  NOBTDERN  BOUNDARY  COMMISSION.  [84] 

TABLE  III— Continued. 


17 

55. 

AJI 

WA. 

A  .,/ 

TA,./ 

Cor.  to 

a 

6 

"l" 

«w 

Bradley. 

o 
279.1 

o 
+39.4 

// 

—  .731 

28.0 

11 

+1.G7 

.60 

ii 
—1.5 

1.0 

// 
—1.6 

7]    Hercnlis  ......  .....* 

248.6 

+39.4 

—  .685 

42.4 

—3.  20 

1.12 

+1.7 

.7 

+  -8 

a    Canuiu  Veuaticornm  . 

191.  1 
277  2 

+39.6 
+38  6 

—  .  055 
+    302 

49.1 
66  1 

—  .87 
—1  63 

1.24 
1  69 

+  .4 
+1.1 

.7 
2.0 

+  .2 
+  .2 

61  Cygni 

314  0 

+37  6 

+    007 

36  9 

+     15 

.83 

-1-  .8 

1.0 

/3    Atdrotnedse   .   . 

14  0 

+34  3 

+  .  2C4 

36  0 

—2  17 

71 

+2.6 

1.0 

+1.7 

3    Trianguli    ...  .  . 

28  8 

+33  8 

—  .284 

20  9 

—  .68 

.59 

+1.2 

1.0 

+  .3 

e    Cvnui 

309  1 

+33.1 

+1  897 

29  4 

—2  61 

93 

+1  9 

.7 

+  .6 

8    Lyra)    ... 

280  3 

+33  1 

+  .  140 

46  2 

—2  10 

1  08 

—  1.7 

1  0 

—2  1 

i     Auriga;    . 

70  3 

+32.8 

—    448 

33  3 

—  1.05 

.77 

+1.  1 

1.0 

+    5 

f    Horculis  

248.0 

+32.1 

+  .039 

29.6 

+  .18 

.78 

+1.5 

.7 

+  -3 

T    Cvcni 

315  6 

+29  2 

—    517 

29  2 

—  .65 

.55 

—  .9 

1.0 

—1.4 

#    Tauri  

77  7 

+28  4 

—     242 

69  4 

+  .35 

1  80 

—  .4 

1.5 

—  2.0 

3    Geniinorum 

112  6 

+28  6 

—    206 

70  3 

—    43 

1  83 

+  .8 

2.0 

+  .3 

a.    Andromedas. 

358  9 

+27.  7 

—     144 

70  4 

—    90 

1  52 

+1.  1 

1.0 

+  .2 

fj.    Herculis  

264.2 

+27.9 

+  .094 

18.2 

—1.94 

.67 

+2.4 

1.0 

+  .6 

e    Bootis  . 

218  6 

+2«  1 

—    121 

32  4 

+    53 

76 

+  .3 

.7 

—  .6 

a    Corona  

231.1 

+27.6 

—  .018 

69.7 

—1.00 

1.83 

+2.9 

1.0 

—1.6 

fj.    Leoois 

144  7 

+27  1 

—    495 

30  8 

+1  23 

64 

—2  5 

1.0 

—1.8 

143  0 

+24  9 

+    046 

30  1 

—1  68 

70 

+1  1 

1.0 

+  .  1 

77    Tauri  

53.2 

+23.3 

—  .190 

30.6 

—  .18 

.57 

—  .7 

1.0 

—  .8 

a    Arietis  

28.4 

+22.3 

—  .128 

70.7 

—  .65 

1.83 

+  .5 

1.0 

—  .3 

(i    Gominornm  

92.0 

+23.  6 

—  .555 

31.7 

—  .03 

.59 

-1.2 

1.5 

—  .7 

5    Geminorum  

106.4 

+22.4 

—  .  172 

30.5 

—2.  38 

.59 

+  .6 

1.0 

•* 

(I    Leouis  

165.3 

+21.9 

+  .  142 

43.2 

—1.61 

1.01 

-.3 

1.0 

—1.0 

j'1   Leonis  

151.6 

+21.1 

—  .331 

35.  7 

—3.11 

.76 

+1.1 

1.0 

0 

a    Bootis  

211.1 

+20.  5 

—  .234 

70.7 

—2.  02 

1.83 

+1.8 

2.0 

+  .3 

ij   -  Bootis  

205.8 

+19.6 

—  .229 

43.4 

—1.22 

1.03 

+  .5 

1.0 

—  .8 

a    Tauri  . 

65  5 

+16  0 

+     060 

71  5 

—    79 

]  HI 

-4-1  7 

2  0 

+  .9 

/3    Leonis  

174.1 

+15.9 

+  .259 

69  7 

—2.44 

1.84 

+1.8 

1.5 

+  .3 

a1   Herculis  ,..   .. 

255  9 

+14  7 

+     197 

70  5 

—    34 

1  84 

+1  4 

1  0 

O 

343  1 

+13  9 

+    330 

70  7 

—  1  82 

1  83 

+2  8 

1  0 

-4-1  7 

v    Pecasi  .  . 

0  2 

+13  8 

231 

60  1 

—     16 

1  82 

—    1 

1  5 

—i  t 

283  5 

+13  5 

+     149 

30  9 

—     67 

72 

+2  1 

1.0 

+     3 

260  9 

+12  8 

4.     in 

70  3 

—  1  05 

1  82 

+3  0 

1  0 

+1.3 

148  8 

+13  2 

+    056 

71  5 

—  1  18 

1  84 

+1  9 

1.5 

+  .4 

293  7 

+  10  0 

+     003 

70  0 

—    25 

1  77 

+  1  2 

1.5 

—  .4 

337  3 

+  96 

—    440 

29  7 

+1  85 

68 

+1  5 

1.0 

+  .3 

K    Ophiuchi  

251  5 

+  98 

—    Oil 

29  8 

—    39 

83 

+  1  9 

1.0 

0 

e     Pecasi  .  . 

323.0 

+  88 

+     037 

23  6 

—    61 

.68 

+1.1 

1.0 

—  .1 

a    Afiuilae  

294  7 

+  82 

+     040 

71  5 

—     10 

1.  P4 

+1.7 

2.0 

+  .2 

(i    Orionis  

85  5 

+  73 

+    019 

71  5 

—  .02 

1  84 

+1  0 

2.0 

+  .1 

e     Piscium  

12  6 

+  6.6 

—    343 

26  1 

4-    32 

.63 

—  1.5 

.7 

—1.6 

e     Hydrse  

128  4 

+  7.3 

—    189 

28  2 

—3  46 

.55 

+3  3 

1.0 

+1.0 

233  1 

-4-72 

+     028 

71  5 

57 

1  84 

4-2  9 

1  0 

-i_l  o 

356  7 

+  55 

515 

35  1 

—    41 

69 

7 

1  0 

—    9 

/?    Aquilce  . 

295  8 

-i_  5  8 

136 

71  5 

—    74 

1  84 

-1-1  5 

1  5 

0 

/      Piscium  .. 

351  8 

+  43 

572 

42  0 

+1  58 

96 

2 

1  0 

—    7 

a     Coti           

42  4 

4-  3  1 

—    207 

71  5 

4-     49 

1  84 

4 

1  0 

—  1  0 

288  3 

+  26 

+     100 

45  8 

—     11 

1  06 

4-3  3 

1  0 

4-1   2 

[85]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          491 

TABLE  III — Contiuued. 


IT, 

£. 

AJ 

""A. 

A/*' 

wAu" 

Cor.  to 

a 

,! 

a/i 

aft 

Bradley. 

y    Ceti  

o 
37.7 

o 
+  2.2 

—  .390 

37.4 

it 
—1.25 

.80 

+  -8 

1.0 

n 
+  -1 

j3    Virginia  ............ 

174.5 

+  3.1 

—  .019 

58.4 

—  .89 

1.41 

+1.6 

1.5 

—  .2 

C     Virginia  ............ 

200.6 

+  0.7 

—  .249 

33.0 

—  .37 

.72 

+1.6 

.0 

+  1.6 

181  8 

-I-  0.7 

—  .425 

25.5 

—  1.  42 

.50 

+1.3 

.0 

—  .4 

6    Orionis 

79  9 

—  0.5 

—  .515 

26.6 

+1.51 

.69 

+  .0 

.0 

—  .4 

335  7 

—  1  4 

—  .603 

17.9 

+1.  8-2 

54 

+1.6 

.0 

+  .4 

328  3 

—  1.5 

—  .009 

71  5 

—  .40 

1.84 

+2.8 

.0 

+1.6 

e     Orionig      .   .      .   . 

80  9 

—  1.4 

—  .221 

24.9 

—1.51 

.56 

+3.5 

.0 

+1.4 

rj     Serpentis 

272  2 

—  2  9 

+  .366 

29  5 

—2.04 

.62 

+1.7 

.0 

0 

6    Opbiucbi 

240  4 

—  3.0 

—  .329 

32.7 

+     48 

75 

+2.3 

.7 

+  .3 

(3    Af[uarii  .  . 

319  7 

—  6  6 

+     196 

28.3 

—  1.  39 

74 

+3.  5 

.0 

+1.0 

a     Hydra?             .    . 

138  9 

—  7  6 

+     128 

69  9 

—  .78 

1  81 

-+-1.6 

.0 

+  .1 

ft    Orionis 

75  7 

—  8  5 

+  .187 

71.5 

—  .01 

1  84 

—  .0 

2.0 

—  .6 

Ol    Ceti 

17  9 

—  9  5 

+     187 

22.1 

—  .87 

63 

+1.2 

.0 

+  .6 

|3    Libra) 

226  0 

—  8  5 

+     066 

34.6 

—1  23 

79 

+2.7 

.0 

+  .4 

a    Virginia 

198  1 

—  9  9 

+    052 

71  5 

—  1.00 

1  84 

+    9 

.5 

—1.2 

o2  Capricorni  ....  ...... 

301.  1 

—13.0 

—  .310 

+  .75 

—  .2 

.0 

—1.4 

J     Crateris  
yl   Eridani  
ft3  Librae  

166.  8 
56.7 
219.3 

—13.  9 
—14.0 
—15.4 

—  .641 
—0.417 
+  .050 



+1.00 
+  .41 
—1.86 



—  .5 
+  .6 
+1.9 

.0 
.0 
.0 

—1.3 
+  -3 

0 

a    Leporis  
/3    Ceti  

jfl1   Scorpii  .  ......  ...... 

80.5 
07.8 
237.8 

—17.9 
—18.8 
—19.4 

—  .098 
—  .301 
+1.620 



—  .13 

+1.  43 

—5.84 

...... 

±'1 
+1.7 

1.0 
1.0 
1.0 

—  .7 
g 

'o 

fil   Sagittarii  
(5    Scorpii  

/?    Corvi  
15  Argua  

270.2 
236.  5 

185.4 
119.3 

—21.1 
-22.2 

—22.  5 
—23.9 

—  .567 
+  .796 

—  .404 
+  .033 



+1.63 
—4.14 

+  .45 
—1.69 



—1.2 

+3.8 

+  -6 
+3.2 

1.0 

1.0 

1.0 
1.0 

—1.0 

+  .8 

—  .7 
+1.3 

«    Scorpii  

e     Canis  Majoris  .  ...  . 

243.  6 
10-2.  2 
341  0 

—26.1 

—28.8 
—30  4 

—  .071 
—  .603 
—    609 



-1.06 
+1.62 
4-1  34 



.+1.2 
+1.1 
—     5 

1.0 
0.5 
1  0 

0 
+  .5 
+  .1 

Columns  one,  two,  and  three  require  no  explanation.  Columns  four  and  five  con- 
tain the  correction  to  the  assumed  declination  for  the  epoch  1845,  with  the  weight  as 
determined  from  the  equations  of  condition.  Column  six  contains  one  hundred  times 
the  correction  to  the  annual  variation  assumed,  and  column  seven  its  weight.  In 
reference  to  the  weights,  it  should  be  remarked,  that  for  the  first  five  stars  the  weights 
were  assumed  on  different  principles  from  those  which  prevail  with  other  stars.  The 
manner  of  assigning  weights  to  the  stars  from  a2  Capricorn!  to  a  Piscis  Australis  has 
been  already  explained.  As  they  are  not,  therefore,  strictly  comparable  with  the  pre- 
ceding they  are  omitted.  Column  eight  contains  the  correction  to  Gh  1752  and  Gh 
1755,  resulting  from  the  preceding  values  of  J  S  and  A  //.  The  process  of  obtaining 
these  corrections  was  this:  The  catalogue  declinations  were  corrected  for  nutation  as 
explained  (p.  20).  The  declinations  between  +  14°  and  —  14°,  have  been  corrected  by 


492 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[86] 


Bessel  for  certain  quantities  necessary  to  make  tbem  agree  with  Bradley's  observations 
of  tbe  sun.    The  following  table  is  given  in  Fundamenta  Astronomia;  (p.  62). 


6 

Correction. 

& 

Correction. 

6 

Correction. 

0 

// 

o 

// 

o 

// 

—  13 

+  -'I 

—  3 

+    .67 

+    7 

+  1.22 

—  11 

+  .63 

—  1 

+  2.36 

+    9 

+     .47 

—    9 

+  .24 

+  1 

+  1.03 

+  11 

+     .93 

—    7 

+  .72 

+  3 

+  1.46 

+  13 

+     .49 

—    5 

—  .0(5 

+  5 

+    .42 

These  corrections  I  have  subtracted  from  the  catalogue  declinations ;  by  which 
means  we  are  able  to  assume  the  same  system  for  all  stars  south  of  Greenwich  zenith. 
The  standard  declination  for  1752  is  equal  to  the  assumed  declination  +  J //'  —  .93  AH'. 
From  the  standard  so  formed  is  subtracted  the  corrected  declination  of  the  catalogue. 
The  result  is  the  "Correction  to  Bradley."  For  the  stars  enumerated  below  the  correc- 
tions to  declinations  from  lower  culmination  are  given  with  reversed  sign,  as  the  above 
table  deals  with  upper  culmination  only. 

Stars  observed  sub  polo. 


Name. 

a  +  180° 

Corr.  to 
Bradley. 

Weight. 

Name. 

a  +  180° 

Cor.  to 
Bradley. 

Weigbt. 

A    Urea  Minoris  . 

o 
139.6 

a 

•4-  .24 

.4 

•y    Cephei 

o 
172.4 

// 
+  .89 

.4 

fl    Ureas  Miuoris  . 

190.9 

—  1.55 

2.0 

i/>    Draconis    ...... 

86.6 

—2.24 

.7 

d    Ura<6  Minoris  . 

102.7 

+1.13 

1.0 

d     I  >ra<:oni.s  .  . 

108.1 

+1.17 

1.0 

Camelop.(32H 

12.0 

—2  74 

1.0 

ij    Draconis    . 

65.2 

—5.  64 

1.0 

e    Ursse  Minoria  . 

78.0 

—  .27 

1.0 

o    Draconis     ... 

101.9 

+2.04 

1.0 

f    Ursee  Minoris  . 

58.3 

—2.85 

1.0 

6    Ursse  Majoris  ... 

319.1 

—  .24 

1.0 

The  ninth  column  gives  the  weight  used  in  solving  the  equations  of  condition, 
following  is  the  scale : 


The 


Obs. 

Weight. 

1 

.4 

2 

.7 

3-9 

1.0 

10-25 

1.5 

over  25 

2.0 

In  estimating  these  weights,  no  account  is  taken  of  the  uucertainty  of  the  standard 
places.  Their  probable  error  seldom  exceeds  ".45,  and  for  the  fundamental  stars 
averages  about  ".3.  The  probable  error  of  the  unit  of  weight  for  the  additional  stars 
is  approximately  ".35. 

Owing  to  the  uncertain  character  of  the  residuals  I  did  not  think  it  safe  to  attempt 
the  drawing  of  a  curve.  Careful  preliminary  examination  showed  that  the  error  varies 


[87 1 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  493 


greatly  with  the  Right  Ascension,  according  to  what  law  it  is  difficult  to  conjecture. 
I  assumed  at  first  the  simple  periodic  formula  of  correction, 

x  sin  a  +  y  cos  a. 

The  form  of  the  declination  correction  (order  of  declination)  especially  for  southern 
stars,  appears  to  be  tolerably  well  represented  by  the  expression — 

v  +  w  sin  2  Z  +  u  tan  Z. 
For  southern  stars  alone  the  normal  equations  are  these : 


+  109.2  v  +  77.2  w  —  0.6 x  +  5.9  y  +  111  0«  -  100.0  =  0 
+  77.2  v  +  63.5  w  —  3.3  x  +  3.9  y  +  82.3  «  —  85.7  =  0 
—  0.60—  3.3  «?  + 59.6  #  +  1.8  y—  9.2  u  +  30.1  =  0 
+  5.9  v+  3.9  10+  1.8  x  +  49.0  y  +  4.2  u  +  8.5  =  0 
+  111.0  v  +  82.3  w  -  9.2  x+  4.2  y  +  245.2  u  -  121.8  =  0 

From  which — 

v  =  -  .21 
IP  =  +  1.50 
x=—  .41 
y  =  -  .25 
u=  +  .08 

Arranged  in  four  nearly  equal  8rollPst  w«  have  the  following  values  of  v,  x,  and 
y,  the  residuals  being  first  corrected  for  +  1".50  sin  2  Z  +  ".08  tan  Z. 


Mean  i 

v 

x 

9 

Weight 
of  i/. 

Adopted  y. 

o 

a 

it 

II 

n 

—  13.0 

—  .20 

—  .17 

—  .88 

10 

—  .98 

+  08.3 

—  .07 

—  .5-J 

—  .72 

16 

—  .48 

+  25.6 

—  .42 

—  .49 

+  .09 

11 

—  .06 

+  43.4 

—  .19 

—  .29 

+  .36 

10 

+  .37 

The  constancy  of  v  and  x  is  as  good  as  we  might  expect,  but  such  is  not  the  case 
with  y.  In  the  uncertainty,  I  have  supposed  y  to  vary  directly  with  the  declination, 
and  find — 


The  equations  for  northern  stars  are : 

// 

+  60.9  v  —  27.6  w  —  13.  L  x  +    0.5  y  —  28.9  u  +  63.8  =  0 

-  27.6  v  +  20.3  w  +    1.3  x  +    0.2  y  +  21.5  u  —  35.2  =  0 
—  13.1  v  +    1.3  w  +  31.1  x  —    1.8  y  —    3.9  u  —  13.7  =  0 
+      .5t>+    0.2  w—    1.8  x  +  29.8  y-    2.8  «+  17.2  =  0 

-  29.0  0  + 21.5  w  —    3.9  x-    2.8  y  +  43.9  u  -  31.5  =  0 


494 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[88] 


Whence —  ' 

«  =  -    .63 

w  =  +  1.25 

x  =  +    .04 

y  =  -    .01 

u  =  -    .35 

The  number  of  stars  and  the  weights  are  too  small  to  admit  of  any  valid  argument 
from  the  process  of  grouping ;  the  residuals,  however,  are  not  remarkably  well  repre- 
sented by  the  formula.  The  real  correction  is  probably  much  more  variable.  The 
equality  of  the  two  values  of  w  derived  from  northern  and  southern  stars  is  quite 
striking.  The  smalluess  of  u  in  each  case  is  an  argument  that  the  refraction  deduced 
by  Bessel  corresponds  well  with  Bradley's  observations.  For  the  definitive  correction 
I  have  dropped  u  and  combined  the  equations  for  both  northern  and  southern  stars. 
Two  sets  of  coefficients  for  sin  a  and  cos  a  are  separately  determined.  For  northern 
stars  these  are  denoted  by  x1  and  y'.  y  is  introduced  into  the  equations  in  order  to 
eliminate  its  mean  influence  on  the  determination  of  the  remaining  quantities. 
The  equations  follow. 


+  170.1  v  +  49.6  w  —  13.1  x1  + 
+  49.6  v  +  83.8  IP  +  1.3  x1  + 
-  13.1  v  +  1.3  w  +  31.1  a'  - 
+  0.5  v  +  0.2  w  —  1.8  a;'  + 


—      0.6  v  —    3.3  *r 
+     5.9  v+    3.9  w 
The  solution  gives : 


0.0  x1 
0.0  x' 


0.5  y'  —    0.6  x  + 
0.2  y'  —    3.3  x  + 
1.8 1/'        0.0  a; 
!9.8  y'        0.0  # 
0.0  y'  +  59.6  #  +    1.8  y  + 
0.0  y'  +    1.8  a;  +  49.6  y  + 


5.9  y  —  36.2  =  0 
3.9  y  -  121.0  =  0 
0.0  y  —  13.7  =  0 
0.0  y+  17.2  =  0 
1.8  y  +  30.1  =  0 
8.5  =  0 


v  =  -    .21  ±  .06 
w  =  +  1.56  ±  .10 


x'  =  +    .25  ±  .16 

y1  =  -    .57  ±  .16 

x  =  —    .41  ±  .10 

y  =  -    -25 

The  probable  error  of  the  unit  of  weight  is  ±  ".79.  For  northern  stars  it  is 
rfc  1".03 ;  and  for  southern  ±  ".65.  These  probable  errors  are  somewhat  larger  than 
can  fairly  be  ascribed  to  Bradley's  declinations,  since  they  include  the  effect  of  the 
prebable  error  of  the  normal  places  themselves.  In  order  to  be  on  the  safe  side  I  have 
adopted  the  following  weights  in  final  discussion,  the  supposed  probable  error  of  the 
unit  being  ±  ".30,  as  will  be  explained  hereafter. 


Weight. 

Number  of  observations. 

Northern  stars. 

Southern  stars. 

00 
.05 
.1 
.:> 
.3 

1 

2  to  8 
9,  or  more. 

1 

2,  or  3 
4  to  20 
21,  or  more. 

[89J 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


495 


In  computing  Table  V.,  weight  .5  is  assigned  to  4  or  more  observations,  and  weight 
.3  to  less  than  that  number.  Declinations  of  Gh  1752-55,  from  one  observation  are 
rejected.  If  the  corrections  above  determined  are  combined  with  those  for  nutation 
we  liave  — 

For  northern  stars  (north  of  51°.5  <5) 

—  ".21  +  1".56  sin  Z  +  ".05  sin  a  -  ".29  cos  «. 
For  southern  stars  (south  of  51°.5  S) 

—  .21  +  1.56  sin  Z  —  ".82  sin  a  —  .24  (28°  —  s\  cos  a. 

Z  is  reckoned  in  the  usual  direction  from  0°  to  360°. 

For  convenience  the  following  tables  have  been  constructed  : 

TABLE  IV. 

Definitive  corrections  for  BesseVs  Fundamenta  Astronomies. 
Northern  stars,  +  51°.5  to  +  90°. 


Correction. 

S 

Above 

Below 

pole. 

pole. 

0 

n 

" 

f50 

— 

.13 

+ 

.82 

55 

— 

.40 

+ 

1 

.06 

CO 

— 

.66 

+ 

1 

.27 

65 

— 

.92 

+ 

1 

.46 

70 

—  1 

.15 

+ 

1 

.60 

75 

-1 

.35 

+ 

1 

.70 

80 

-1 

.52 

+ 

1 

.76 

85 

-1 

.65 

+ 

1 

.77 

90 

J 

.73 

+ 

1 

.73 

NOTE.  —  The  corrections  are  applicable  to  declina- 
tions directly,  whether  observed  above  or  below 
pole.  The  entire  correction  for  northern  stars  is 
A  +  B. 


a 

Corr. 

a 

h 

// 

h 

0 

-.29 

12 

1 

-.27 

13 

2 

-.23 

14 

3 

-.17 

15 

4 

-.10 

16 

5 

-.03 

17 

6 

+  .05 

18 

7 

+  .12 

19 

8 

+  .19 

20 

9 

+  .24 

21 

10 

+  .28 

22 

11 

+  .30 

23 

12 

+  .29 

24 

From  12b  to  24b  the  correction  has  the  opposite 
sign. 


496 


UNITED  STATES  NOETHEEN  BOUNDAEY  COMMISSION. 


[90J 


C*. 

For  stars  south  o/51°.5<5. 


A.E. 

DECLINATION. 

+50° 

+45° 

+40° 

+35° 

+30° 

+25° 

+20° 

+15° 

+10° 

+05° 

+00° 

-05° 

-10° 

-15° 

-20° 

-25° 

-30° 

0 
1 
2 
3 

it 
+  .92 
+  .70 
+  .49 
+  .31 

f  .42 
+  .18 
-  .07 
-  .33 

+  .56 
+  .34 
+  .09 
-  .15 

+  .71 
+  .48 
4-  .25 
-1-  .03 

+  .82 
--  .60 
--  .3!) 
+  .19 

f:B 

Iia 

+1.01 
+  .60 
+  .61 
+  .47 

+  .99 
+  .78 
+  .61 
+  .49 

+  .93 
+  .73 
+  .57 
+  .46 

f  .82 
+  .62 
+  .48 
+  .39 

+  .C6 
+  .46 
+  .33 
+  .26 

+  .46 

+  .27 

+  -14 
+  .10 

+  .21 
+  .02 
-  .09 
-  .12 

-  .08 
-  .26 
-  .36 
-  .37 

-  .40 
-  .5t 
-  .07 
-  .66 

-  .75 
-  .92 
-1.00 
—  .91 

—  1.  12 
-1.29 
-1.35 
—1.31 

4 

5 
6 

-  .58 
-  .79 
-  .96 

-  .37 
-  .55 
-  .69 

-  .17 
-  .32 
-  .43 

+  .01 
-  .11 
—  .19 

+  .16 
+  .06 
+  .02 

+  .29 
+  .22 
+  .21 

+  .37 
4-.  33 
+  .34 

+  -41 
+  .40 
+  .45 

+  .41 
+  .43 
+  .50 

+  .36 

+  -41 

+  .52 

+  .26 
+  .34 
+  .46 

+  .12 

+  .23 
+  .40 

—  .07 
+  .06 
+  .27 

-  .30 
-  .14 
-  .10 

-  .5fi 
-  .37 
-  .10 

-  .85 
-  .03 
-  .33 

-1.16 
—  .91 
—  .58 

7 
8 
9 

-1.08 
-1.13 
-1.10 

-  .77 
-  .79 
-  .75 

-  .48 

-  .48 
-  .41 

—  .21 

-  .18 
-  .OS 

+  .03 
+  .09 
+  -21 

f  .25 
•f.  34 
+  .49 

f  .42 
+  .54 
+  -71 

+  .55 
+  .70 
+  .90 

+  .64 
+  .K 
+1.04 

+  .69 
4-  .89 
+1.14 

+  .66 
+  .91 
+1.1* 

+  .62 

T.b9 
+1.19 

+  .53 

4-  .82 
+1.14 

f  .39 

+  .71 
+1.00 

+  .22 
+  .57 
+  .94 

+  .02 
1.40 
+  .80 

-  .20 
+  .22 
+  .63 

10 
11 
12 

-1.02 

-  .87 
-  .68 

-  .65 

-  .49 
-  .29 

-  .28 
-  .11 
+  .09 

+  .00 
+  .24 
+  .45 

+  .37 
+  .57 

+  .78 

+  .67 
+  .88 
+1.0C 

+  .91 

+1.13 
+1.35 

+1.12 
+1.34 
+1.57 

+1.28 
+1.52 
+1.75 

+1.39 
+1.65 

+1.88 

+1.4C 
+1.72 
+1.96 

+1.48 
+1.76 
+2.00 

+1.45 
+1.77 
+1.99 

+1.39 
+1.69 
+1.94 

+1.29 
+1.61 
4-1.86 

+1.17 
+1.49 
+1.75 

+1.02 
+1.30 
+1.62 

13 

14 
15 

-  .44 

-  .19 
-  .07 

-  .06 

+  .19 
+  .43 

+  .32 
+  .55 

+  .77 

+  .68 
+  .89 
+1.09 

+1.00 
+1.21 
+1.39 

+1.31 

+1.50 
+1.66 

+1.56 
+1.75 
+1.89 

fl.78 
+1.95 
+2.07 

+1.95+2.08 
+2.11+2.22 
+2.22+2.31 

+2.15 
+2.2C 
+2.36 

+2.19 
+2.32 
+2.36 

4-2.18 
+2.29 
+2.32 

+2.12 
+2.22 
+2.  23 

+2.04 
+2.13 

+2.12 

+1.92 
+2.00 
+1.97 

+1.79 
+1.85 
+1.81 

16 
17 
18 

f  .32 
+  .53 

+  .70 

+  .65 
+  .83 
+  .97 

+  .97 
+1.12 
+1.23 

+1.27 
+1.39 
+1.47 

+1.52 
+1.64 
+1.08 

+1.79 

4-1.  w 

+1.87 

+1.99 
+2.03 
+2.01 

+2.15 
+2.10 
+2.11 

+2.27 
+2.25 
+2.19 

+2.34 
+2.29 
+2.18 

+2.36 
+2.28 
+2.14 

+2.34 
+2.23 
+2.  06 

+2.27 
+2.13 
+1.93 

+2.16 
+2.00 
+1.76 

+2.03 
+1.83 
+1.56 

+1.85 
+1.63 
+1.33 

+1.66 
4-1,41 

+1.08 

19 
20 
21 

+  .82 
£.87 
+  .84 

+1.05 
+1.07 
+1.03 

+1.28 
fl.28 
+1.21 

+1.49 
+1.46 
+1.36 

+1.67 
+1.61 
+1.49 

+1.83 
+1.74 
+1.59 

+1.94 
+1.82 
+1.65 

+2.01 
+1.86 
+1.06 

+2.  04  +2.  01 
+1.  86  +1.  81 
+1.  64  +1.  56 

+1.9: 

+1.71 
+1.44 

+1.84 
+1.59 
+1.27 

+1.67 
+1.38 
+1.06 

+1.47 
+1.15 
-f  .80 

+1.24 
+  .89 
+  .52 

+  .98 
+  .60 
4..H 

+  .70 
+  .29 
-  .13 

22 
23 
24 

f  .76 
+  .61 
+  .42 

+  .93 

I  is 

+1.08 
1.91 
4-.  71 

+1.22 
+1.04 
+  .83 

+1.33 
+1.13 
+0.92 

+1.41 

+1.20 
+  .99 

+1.45 
+1.23 
+1.01 

+1.44 
+1.  22 
+  .99 

+1.40 
+1.16 
+0.93 

+1.31 
4-1.05 
4-0.82 

J1.1C 
.!!() 
.66 

+  .98 

•f  .70 

+  .46 

+  .75 
+  .45 
+  .21 

f  .47 
+  .1' 
-  .08 

+  .17 
-  .15 
-  .40 

-  .17 
-  .49 
-  .75 

-  .52 

-  .85 
-1.12 

*  Between  +14°  and  — 14°,  S,  the  entire  correction  is,  C+  correction  taken  with  opposite  sign  from 
table,  p.  62,  Fund.  Ast. 

SECTION  VIII. 

DISCUSSION  OP  FINAL  CORRECTIONS  AND  WEIGHTS. 

With  the  correction  just  deduced,  we  shall  be  able  to  add  a  considerable  number 
of  standard  stars  to  the  list  embraced  in  Table  III.  The  places  of  the  four  extieme 
southern  stars  of  Table  I.,  as  well  as  the  additional  stars  of  Table  III.,  will  be  revised 
by  the  addition  of  Gh,  1752  or  '55,  as  an  authority.  Forty  fundamental  and  circuin- 
polar  stars  of  Table  I.  would  not  be  materially  affected  by  this  addition.  For  tho 
present,  their  declinations  as  already  corrected,  will  be  regarded  as  standard. 

Two  or  three  stars,  which  should  have  been  included  in  the  list,  were  omitted  by 
accident. 

The  manner  of  deducing  A  S  and  A  p!  has  been  sufficiently  explained  under  sections 
VI.  and  VII.  Their  values  will  be  found  to  be  not  materially  different  from  those 
finally  deduced. 


[91]  EBPOET  OP  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 

TABLE  V. 


497 


Values  of  AS  and  A/J.'  adopted  in  computing  final  systematic  corrections  for  the  principal 

catalogues. 


18 

45. 

18 

45. 

Ar> 

Au' 

A<5 

V 

o,    Atidromedse  -  ....  ....  .... 

if 

—  .14 

II 

—  .90 

n    Leporis  .  ,_„._.  

// 
—     14 

// 

4    17 

(3    CassiopesB  ...........  .. 

—  .31 

41.11 

e     Oriouis  .  .  .  .  ....  

—    35 

24 

—  .23 

—  .16 

a.    Orioois  

_L    02 

02 

—  .13 

4  -47 

{3    Auricse  .  . 

—  .05 

60 

4  .02 

—  .43 

0    Ceti  

—  .28 

41.20 

—    02 

-4-    21 

ij    Cassiopeae  .     .     .... 

—  1.20 

41.62 

—    46 

1  15 

y    Cassiopesa  ......  .... 

—  .39 

•    42.  G8 

y    Geminorum  

j_    24 

1  f>9 

e    Pisciuni  ......  ...... 

—  .26 

.39 

Cephei,  (51H)  

4     12 

67 

(3    A  iid  romoduo  .....  . 

4  .24 

—1.97 

—    67 

42  oo 

+  .09 

—  .26 

C    Gennnorum  ...  ......  .... 

4-    72 

1  54 

4  .06 

4  .82 

d    Geminorum  .... 

17 

2  48 

0i   Ceti  

+  .13 

—  .39 

4    09 

73 

—  .52 

—2.36 

4    81 

1  51 

51  Andromeda? 

—  .35 

4-  .06 

(3    Geminorum  . 

21 

43 

54  Andromedae 

4  .43 

—2.92 

4    01 

1  49 

o    Piscium          .... 

.13 

—1.59 

o    Avsrus  .. 

10 

62 

e     Cassiopcjjo     ..... 

4  .18 

4  .25 

—    31 

4-    04 

(3    Arietis      .       .   ..... 

—    04 

—  1.76 

o    Ursaj  Majoris.    ...... 

4    06 

_i_    95 

50  Caesiopea3  .... 

4     44 

42.02 

6    Cancri   .  ......  ...... 

4    03 

1  08 

y    Andromedae  ... 

4  .26 

4  .96 

e    Hydrse  ...  ....  ...... 

27 

2  54 

a    Arietis          .      ... 

—  .13 

—  .65 

i     Ursa)  Majoris  .  ...... 

27 

22 

{3    Trianguli     ......... 

—  .31 

—  .38 

<72  UrssB  Majoris  ....... 

4    78 

44  46 

ft   Ceti  

4  .04 

—  .57 

K    Cancri  

12 

2  72 

f3  Ceti  .  ;  

13 

4  .40 

12 

20 

y    Ceti  

40 

—  1.14 

4    13 

78 

a    Ceti           

—   .21 

4  .49 

0    Ureas  Majoris  ..  ...... 

33 

4    60 

/?    Persei  

4    44 

—  .92 

4    47 

60 

a    Persei      .     .       .... 

.23 

4-  .33 

4     03 

1  57 

f    Tauri  

41.37 

4  .58 

v    Ursse  Majoris  

4  .33 

—  .20 

25 

4    04 

u     Loon  is..  _.  ..... 

39 

15 

—  .13 

—  .84 

o,    Leonis  ....  ....  ......  .... 

4  .06 

—1.18 

44 

4    66 

/I    Ursse  Majoris          .  . 

58 

41  46 

c    Tauri 

4     18 

—1  35 

33 

3  10 

4    06 

—    79 

a    Ursaj  Majoris  .  .  .... 

4    26 

1  11 

4    25 

4    20 

28 

1  11 

•f-    36 

—2  12 

36 

2  26 

47 

—    76 

(3    Ursa3  Majoris..   .... 

4    29 

2  16 

(3    Camelopardalis  ...  . 

4  .23 

—  .12 

a    Ursse  Majoris  

4  .02 

—  .45 

e     Auri"8B  .  . 

4  .13 

—  .91 

T/J    Ursa  Majoris  

—  .15 

—  .54 

4  .23 

—  1.14 

6    Leonis  

4  .19 

—2.09 

4-    01 

—    58 

6    Crateris  ...... 

—    59 

4    30 

4-     19 

—    01 

—    14 

—  1  80 

(3    Tauri  

—  .24 

4  .35 

A    Draconis  

4  .42 

43.2S 

—  .48 

—1.18 

N  B 32 


498         UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.  [92] 

TABLE  V — Continued. 


18 

15. 

18 

15. 

Ac? 

AM' 

M 

V 

v    Leonis  ......       .,... 

n 

—  .G8 

// 
-f  1.  08 

a 

+  .35 

a 
—2.31 

%    UrsoB  Mfljoris     ..   . 

-4-    04 

—  .43 

+  .19 

—  .63 

$    Leon  is 

4-  .26 

—2.  44 

+  .20 

—  .34 

/?    Virginia  ...  ..           . 

—  .01 

—1.00 

p3  Herculia  ....  ....  ....  ..., 

-.11 

—1.14 

y    UrsfB  Majoris  .          .     . 

+  .20 

—    25 

+  .13 

+  .41 

—  .40 

—2.54 

+  .11 

1.05 

—    14 

16 

—  .31 

+1.76 

j?    Virginia  ................ 

—  .39 

—1  76 

+  .02 

1.47 

fi    Corvi  

—  .34 

—  .06 

—  .01 

+  .59 

—  .63 

+2.80 

—  .05 

+  .35 

B.A.C.4342  

•4-  .57 

+3.83 

—  .42 

+  .34 

-4-  .31 

+3.43 

+  .01 

+  .66 

<z    CauumVeDaticorum.  .... 

—  .06 

—  .83 

+  .36 

—2.02 

—  .08 

—2.54 

+  .46 

+  .08 

+  .05 

—1.00 

+  .36 

—1.63 

+    00 

+    35 

e1   LyrsB           .    .   . 

—  .68 

+  .91 

33 

—  2  70 

+  ,21 

—2.85 

+  .10 

—1.01 

—  .02 

—  .05 

—  .21 

—1.45 

+  .25 

—  .84 

+  .23 

+  .22 

e     Aquilse  

—  .23 

+  .35 

—  .23 

—2.02 

A    Aquilse  

+  .13 

—  .73 

X    Bootis  

—  .4:t 

+1.03 

+  .13 

—  .47 

0     Bootis  

—  .14 

—  .70 

+  •  11 

+  .81 

+  .22 

—  1.14 

K    Cygni  . 

—  .33 

+  .60 

4-1.  0^ 

—1.41 

T    Draconis  

+  .42 

+1.17 

4-  .63 

+3.32 

6    Aqnilsa  

+  .05 

+  .45 

—  .09 

4-  .28 

<a    Cygni  

—  .03 

—  .43 

+  .05 

—1.87 

*    AquiliB  

—1.27 

—2.84 

—  .07 

+1.05 

Q    Cygni  

—  .45 

+1.85 

—  .02 

—  .70 

•y    Aquilie  „„  

+  .00 

—  .25 

4-  .04 

—  .97 

£    CvEmi  .. 

+  .20 

—2.61 

—  .30 

—  .57 

+  .04 

—  .10 

—  .10 

—  .13 

—  .14 

—  .74 

4-    12 

—    28 

%,    UrssB  Minoris 

+  .26 

+1.18 

—    02 

1  00 

o2  Cvtrni 

—  .21 

+  .40 

4-    03 

—    57 

GS  Capricorn!   ..... 

—  .30 

+  .53 

—    22 

1  85 

+  .36 

+2.50 

—    13 

—    39 

+  .42 

—1.97 

4-    61 

—  2  74 

o    Cepbei     .       .     ......... 

4-  .10 

+  -74 

/31  Scorpii 

+1  62 

5  77 

d    Delpbini  ......  ....  ..  .... 

+  .61 

—1.76 

+    03 

4-    73 

+  .03 

—  .88 

34 

+    r>9 

+1.89 

—2.41 

30 

36 

39 

+1  37 

—    03 

1  20 

—  .68 

2.81 

4-    16 

48 

—2.  57 

+1.41 

15  Drdconis......  ....   .. 

4-    01 

4-    84 

O^Cygni  

+  .61 

+  .10 

.  17 

4-     45 

C    Cvcni  .. 

.45 

—1.39 

£    Herculis  ........         ... 

+    03 

4-    28 

—  .07 

+1.68 

ij    Herculis  ....   ....... 

—  .69 

—  3  00 

+  .07 

—  .34 

K    Ophiuclii  

—  .01 

—    39 

(3    Cephei          

—  .01 

+1.33 

[93J  REPORT  OF  THE  (JHIEF  ASTRONOMER,  APPENDIX  H.  499 

TABLE  V— Continued. 


18 

45. 

18 

45. 

Arf 

v 

A(J 

<v 

e    Pegasi  

// 
-f  .04 

// 

—  .65 

.5    Pegasi  

// 
—  .46 

// 

+2.01 

v    Cephei  ........  . 

—    13 

-1-1  20 

—    10 

—    01 

16  Pogaei  ......     ..  . 

4-    OC 

—  .72 

a.     07 

4-1  20 

a    Aquarii  .....             .     .  . 

—    10 

—  .40 

.37 

—  2  07 

£    Cephei  . 

4-    24 

—1.09 

—    66 

+1  75 

—  .36 

—  1  53 

-f  .33 

—  1  62 

—  .16 

-1-  .49 

4-    53 

4-4  63 

<J3  Cephei  

4-  .00 

+1.77 

—  .54 

4-1.21 

a    Lacertsa  . 

4-  .  Orf 

—  .43 

4-  .04 

4-1  12 

ij    Aquarii  

—  .66 

+2.  20 

—  .47 

—1.04 

The  general  condition  in  the  selection  of  the  stars  of  Table  V.  is,  that  the  weight  of 
A  /i'  as  determined  by  the  adopted  weights  (p.  72)  shall  be  at  least  .5.  In  two  or  three 
instances  it  fell  below  this  amount  by  trifling  quantities.  Column  €„  "Details  of  Cor- 
rections to  Assumed  Declinations,"  contains  the  values  of  (7,  corrected  for  the  proper 
quantities  taken  from  Tables  II.  and  IV.  From  these  A  S  and  A  p'  are  computed. 
With  the  help  of  A  S  and  A  /*',  the  correction  to  the  assumed  declination  was  computed 
for  every  epoch  required.  Denoting  these  corrections  by  A  d',  we  have: 

r  =  A  d'  —  C. 

These  are  the  corrections*  to  various  catalogues  given  by  the  standard  declina- 
tions of  Table  V;  and  from  these,  arranged  by  catalogues  and  successively  in  the 
order  of  declination  and  right  ascension,  the  definitive  systematic  corrections  are 
derived  for  all  catalogues  ;  a  fevr  excepted  which  were  of  small  weight,  or  which  con- 
tained few  observations  of  standard  stars. 

Determination  of  Definitive  Systematic  Corrections  and  iceights. 

For  convenience  the  residuals  were  combined  in  groups  embracing  generally  not 
more  than  5°,  when  discussed  in  order  of  declination,  and  two  hours  in  order  of  right 
ascension.  To  effect  these  combinations,  weights  are  assigned  in  each  particular  case, 
which  are  based  either  on  special  investigations  made  in  this  paper,  or  elsewhere;  or 
upon  an  empirical  law  derived  from  a  consideration  of  the  circumstances  surrounding 
the  observations,  or  their  reduction.  The  usual  form  of  this  law  has  been  : 


Where  13  is  the  probable  error  of  a  single  observation,  or  of  the  unit  of  weight,  and 
the  other  quantities  have  the  same  signification  as  in  the  discussion  of  Washington 


*  For  the  values  of  r  consult  "  Details  of  Corrections,"  etc. 


500          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.  [94] 

declinations  (p.  4G).    For  the  ratio  — ,  an  integer  was  always  used,  since  it  must  nee- 

£/ 

essarily  be  a  mere  approximation.  The  weights  attached  to  means  of  groups  were 
made  use  of  in  the  graphic  process,  by  means  of  which  the  corrections  in  order  of 
declination  are  invariably  deduced.  The  choice  of  scale  in  plotting  the  residuals, 
depends  upon  the  accuracy  of  the  catalogue  places  under  consideration,  and  was 
always  such,  that  the  relative  weights  could  be  clearly  represented  by  circles  drawn 
about  the  points  to  which  they  respectively  belong. 

It  was  my  original  intention  to  investigate  nearly  all  the  corrections  by  the  use  of 
periodic  formulae;  but  the  time  at  my  disposal  proved  too  limited  for  the  purpose,  and 
it  may  be  doubted  whether  such  a  course  is  really  desirable  for  the  corrections  which 
depend  upon  the  order  of  declination. 

Extreme  accuracy  is  not  to  be  expected  in  the  corrections  derived  from  graphic 
process.  The  temptation  to  make  abrupt  changes  in  direction  of  the  curve,  in  order 
to  represent  what  may  be  mere  accidental  accumulation  of  errors,  has  been  steadily 
resisted.  On  the  other  hand,  where  even  a  slight  peculiarity  is  found  to  be  persistent 
for  a  number  of  catalogues  under  the  same  circumstances  (i.  e.,  at  the  same  observa- 
tory or  with  the  same  instrument),  it  has  been  respected.  Such  peculiarities  have  been 
noticed  in  the  later  Greenwich  and  Radcliffe  catalogues,  and  in  others.  Theoretical 
considerations  have  sometimes  received  weight  in  deciding  the  general  direction  of 
curves,  especially  where  refraction  exerts  an  important  influence. 

Corrections  depending  on  right  ascension  Tiave  generally  been  viewed  with  suspi- 
cion. In  many  cases,  however,  they  are  important  and  clearly  indicated,  and  in  others 
they  might  have  been  safely  expected.  Where  the  correction  appears  to  follow 
approximately  the  same  law  in  successive  catalogues  of  the  same  series  we  may  adopt 
it  without  hesitation.  The  separation  of  the  residuals  into  two  or  more  zones  has 
always  been  made  before  accepting  a  correction  as  definitive. 

The  adopted  form, — 

#  sin  a  +  y  cos  a, 

has  some  support  in  theory,  and  is  here  invariably  adopted  in  corrections  of  this  class. 

Corrections  to  Declinations  from—  30°  to  —90°. 

The  continuation  of  the  curves  of  correction  from  —  30°  to  —  90°  offers  only  a 
rough  approximation. 

The  corrections  to  C.  G.  H.  31,  S.  H.  31,  C.  G.  H.  33,  So  51,  So  55,  C.  G.  H.  58,  Me  62, 
and  Me  G8,  were  first  approximately  determined  between  the  limits  —  10°  and—  30°. 
These  approximations  are  almost  identically  those  of  the  final  table,  and  are  formed 
on  the  same  basis — the  only  difference  being  that  the  general  direction  of  the  curve 
of  correction  was  better  ascertained  after  its  approximate  character  was  known  for 
the  southern  limit.  A  value  of  the  correction  being  assumed  for  declination  —  30°, 
the  remaining  values  were  directly  interpolated  from  this  point,  so  as  to  have  the  value 
zero  at  declination  —  90°.  These  preliminary  values  are  in  some  cases  quite  different 
from  those  of  the  definitive  table  (IX.).  The  following  table  contains  these  prelimi- 
nary corrections  as  actually  used.  Under  the  designation  of  each  authority,  is  also 
given  the  weight  assigned  to  it  in  the  discussion  of  J  S  and  A  /.  When  the  number 
of  observations  is  three  or  four,  the  weight  is  one-half  that  which  otherwise  would 


[95] 


REPOET  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


501 


Lave  been  assigned ;  \vhen  it  is  two,  the  weight  is  three-tenths,  and  one  observation  is 
always  rejected. 

TABLE  VI. 


s 

C.G.H.31. 

S.  H.  31. 

C.G.H.33. 

So  51 

So  55 

C.G.H.58. 

Me  62. 

Me  68. 

0 

// 

// 

// 

// 

// 

// 

// 

—  30 

00 

+  .50* 

+  .90 

+  .80 

—  .50 

00 

+  .87 

—  .57 

—  40 

00 

+  .42 

+  .75 

+  .67 

—  .42 

00 

+  .73 

—  .48 

—  50 

00 

+  .34 

+  .60 

+  .r,3 

—  .34 

00 

+  .58 

—  .38 

—  CO 

00 

4-  .25 

+  .45 

+  .40 

—  .25 

00 

+  .44 

—  .29 

—  70 

00 

-f  -17 

+  .30 

+  .26 

—  .17 

00 

+  .29 

—  .19 

—  80 

00 

+  .08 

+  .15 

+  .13 

—  .03 

00 

+  .15 

—  .10 

—  90 

00 

+    00 

00 

00 

00 

00 

00 

00 

Weight.. 

1 

1 

2 

2 

2 

2 

4 

2 

3 

*  The  corrections  S.  H.  31  are  applicable  directly  to  catalogue  places. 

For  convenience,  the  epoch  of  A  S  is  taken  for  these  few  stars  at  1850.  The  values 
of  A  S  and  A  //  thus  determined,  are  shown  in  Table  VII.,  which  contains  only  stars 
whose  declinations  are  given  both  in  S.  H.  31  and  C.  G.  H.  33. 

TABLE  VII. 
First  approximation  to  AS  and  A/J.'  for  stars  between  —  30°  and — 90°. 


Star's  name. 

A<J  1850. 

T.  t 

A  0 

V 

v 

(3   Hvdri  

// 

—  .02 

17.7 

II 

4-     57 

32 

-1-  .27 

7  1 

—2  71 

18 

+  .33 

15  9 

—1  13 

32 

0i  Eridani 

13 

10  5 

81 

22 

34 

15  9 

27 

32 

4-    07 

11  3 

85 

25 

43 

17  7 

4-1  32 

32 

05 

fe  5 

'70 

21 

4-     32 

10  5 

2  13 

22 

33 

12  9 

4-1  30 

25 

—  .08 

16  2 

—    43 

28 

p  Charoeleontis  ...  ...... 

4-  .31 

16  1 

+    04 

27 

a1  Crucis  ................ 

4-  .  15 

12  6 

—  2  69 

29 

(3   Centauri  

+1.13 

16.4 

—5.27 

.32 

a2  Centauri....    ......   . 

4-    51 

13  0 

—  8  28 

22 

a   TriaDg.Austra.lis  . 

4-  .72 

14  4 

—  4  58 

27 

rj    Scorpii  .   .......     .... 

—  .42 

9.4 

4-    23 

20 

<T   Octantis  

[+.H] 
4-  .46 

"i\'i" 

[-  .76] 
—  2  29 

26" 

—  .37 

12.7 

4-2  06 

28 

I  estimate  the  probable  error  of  the  unit  of  weight  to  be  ±  .4.  This  would  give 
for  average  probable  error  of  A  d  ±  .1,  and  for  A  //  ±  .8. 

In  discussing  the  probable  error  of  the  unit  of  weight  for  each  catalogue,  the  stars 
from  —  30°  to  —  90°  were  not  used  in  any  case. 


502 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[96J 


Discussion  of  Individual  Catalogues. 

The  examination  of  the  systematic  corrections  and  probable  errors  of  each  catalogue 
will  uow  be  presented.  A  brief  explanation  will  probably  suffice  to  make  the  process 
easily  understood.  The  relative  weights  of  the  individual  values  of  r  for  a  given 

catalogue,  were  first  assigned,  usually,  by  deciding  upon  a  value  for-i.     The  following 

ei 

table  is  constructed  with  the  arguments,  number  of  observations,  and  -,  where  e  is  that 

! 
part  of  the  probable  error,  which  is  supposed  to  diminish  in  proportion  to ..        ,  n 

v  n 

being  number  of  observations,  and  c,  the  minimum  probable  error,  or  probable  error 
when  n  is  a  maximum. 

TABLE  VIII. 


£  =2 

•;r* 

-  «=4 

n 

•K1 

n 

'tf 

ra 

* 

1 

1 

1 

1 

1 

1 

2  and  3 

2 

2 

2 

2 

2 

4 

2.5 

3 

2.5 

3  and  4 

3 

5  to  9 

3 

4 

3 

5 

4 

10  to  35 

4 

5  to  7 

4 

6  and  7 

5 

36,  or  more. 

5 

8  to  11 

5 

8  and  9 

6 

12  to  16 

6 

10  to  12 

7 

17  to  27 

7 

13  to  16 

8 

28  to  51 

8 

17  to  20 

9 

52,  or  more. 

9 

21  to  25 

10 

26  to  33 

11 

34  to  44 

12 

45  to  62 

13 

63  to  92 

14 

93,  or  more. 

15 

With  the  chosen  weights,  the  values  of  r  were  combined  in  order  of  declination 
into  convenient  groups,  ra,  embracing  generally  not  more  than  5°  of  declination.  From 
these  the  curve  is  carefully  drawn.  The  values  in  column  Co  are  taken  from  this  curve. 

The  outstanding  residuals  r'  (formed  by  subtracting  from  the  individual  values  of 
r  the  correction  from  the  curve)  are  then  arranged  in  order  of  right  ascension  and  in 
groups,  embracing  each  about  two  hours.  Mean  a  is  usually  given  to  nearest  hour, 
unless  the  fractional  difference  is  more  than  two  or  three  tenths.  In  discussion,  the 
nearest  degree  of  a  was  taken.  In  order  to  facilitate  examination,  the  corrections  in 
order  of  a  have  been  in  all  cases  arranged  in  two  or  more  zones  of  declination,  but 
where  such  an  arrangement  is  of  no  particular  interest  it  is  here  omitted. 

In  a  few  cases  the  correction  in  order  of  declination  has  been  rediscussed  after 
subtracting  from  r  the  respective  values  of  x  sin  a  +  y  cos  a,  but  this  has  not  usually 
been  considered  necessary. 

Following  the  discussion  of  correction  of  each  catalogue  is  a  statement  of  the 
probable  error,  derived  from  the  outstanding  residuals  after  subtracting  the  proper 


[97] 


REPORT  OP  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


503 


systematic  correction  from  the  separate  values  of  r.  The  result  of  no  star  was  taken, 
which  at  the  given  observatory  culminates  at  a  zenith  distance  greater  than  70°. 
These  probable  errors  are  somewhat  too  small  for  the  catalogues  used  in  forming  Table 
V.,  and  slightly  too  large  for  all  others.  The  former  difficulty  is  remedied  in  a  few 
instances  by  the  adoption  of  probable  errors  founded  on  special  discussions.  Kg  21, 
Dt  24,  Pa  45,  Wn  68,  and  Wn  72,  are  examples  of  this  kind.  These  probable  errors 
are,  of  course,  not  the  absolute  probable  errors ;  they  express  simply  liability  to  fortu- 
itous errors,  after  systematic  corrections  have  been  applied.  They  are  required  for 
the  purpose  of  constructing  a  table  of  relative  weights  to  be  used  in  the  discussion  of 
definitive  places. 

In  deriving  the  probable  error  (H)  of  a  single  observation,  a  quantity  m  was  always 
subtracted  from  the  number  of  residuals  before  dividing  the  sum  of  squares  multiplied 
by  weights — that  is,  the  probable  error  of  the  unit  is  derived  on  the  estimate  that  an 
equal  degree  of  accordance  could  have  been  secured  with  a  formula  of  correction  con- 
taining m  terms. 

Po  1800. 

Each  declination  is  supposed  to  be  entitled  to  the  same  weight.  The  groups 
embrace  each  about  2°  of  3. 

Residuals  in  order  of  declination. 


Mean  6 

71-' 

n> 

Co 

Mean  i! 

;r' 

rv> 

Co 

o 

// 

// 

o 

// 

II 

+  86.7 

5 

—  .23 

.00 

+  23.9 

4 

—  1.70 

—  1.22 

+  76.3 

6 

+  .90 

.00 

+  22.  1 

0 

—    .88 

—  1.27 

+  7-2.0 

5 

—  .71 

.00 

+  19.6 

6 

—    .94 

—  1.41 

-j-  69.5 

4 

—  .54 

.00 

+  15.3 

8 

—  2.02 

—  1.83 

-f  67.2 

4 

+  .26 

.00 

+  13.5 

5 

—  2.  17 

—  1.85 

+  65.3 

2 

+  .15 

.00 

+  10.3 

9 

—  1.79 

—  1.61 

+  62.0 

7 

+  .35 

.00 

+    8.4 

8 

—  1.35 

—  1.36 

-f  59.7 

8 

—  .11 

.00 

+    6.6 

5 

—    .20 

—  1.20 

+  57.3 

8 

—  .24 

—  .05 

+    3.6 

7 

—    .71 

—  1.13 

+  55.3 

3 

+  .12 

—  .05 

—    0.5 

7 

—  2.04 

—  1.59 

+  52.4 

7 

+  .19 

—  .15 

—    3.6 

5 

—  a.  72 

—  2.04 

+  49.4 

7 

—  .60 

—  .22 

—    7.2 

3 

—  2.  20 

—  2.24 

+  46.8 

5 

—  .30 

—  .40 

—    9.1 

7 

—  1.76 

—  2.  22 

+  44.5 

0 

—  .82 

—  .54 

—  14.1 

4 

—  2.40 

—  1.79 

+  41.7 

5 

—  .24 

—  .90 

—  18.7 

3 

—     .80 

—  1.25 

+  39.5 

7 

—1.19 

—1.04 

—  22.  4 

4 

—  1.12 

—  1.05 

+  37.7 

3 

—3.  33 

-1.19 

—  27.1 

3 

—  1.08 

—  1.00 

+  34.0 

6 

—2.  05 

—1.44 

—  30.0 

1 

—  1.40 

—  1.00 

+  31.  4 

3 

—1.19 

—1.45 

—  35.0 

2 

+    .08 

—  1.00 

+  28.4 

6 

—  .77 

—1.30 

—  42.1 

5 

—  2.21 

—  1.00 

-f  26.6 

4 

—1.33 

—1.23 

In  drawing  the  curve  much  assistance  was  derived  from  the  comparison  of  Ao  29 
and  Po  1800,  made  by  Argelandcr  (Abo  Catalogue,  p.  xi).  If  we  denote  by  0  the  cor- 
rection to  Gh  1755,  and  by  ft'  the  definitive  correction  to  Ao29  (Table  IX.),  we  shall  have 

on  90 

fr  (,9  —  ft')  + ,<?'  for  stars  south  of  51°.5  declination,  and  ^  (ft  — ft')  +  ft'  for  the  remain- 
der, as  the  correction  to   be  applied  to  the  comparison.    The  drawing  of  the  curve 
proved  to  be  extremely  difficult,  but  its  values  are  adopted  in  the  discussion  of  all 
stars  except  the  few  reserved  for  treatment  with  catalogues  of  Class  III. 
The  separate  outstanding  residuals,  grouped  in  the  order  of  a,  give: — 


504 


UNITED  STATES  NOETHEEN   BOUNDAEY  COMMISSION. 
Residuals  in  order  of  right  ascension. 


[98] 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +  40° 

—  30°  to  +  6° 

—  30°  to  +  90° 

Mean  a 

TT' 

'V 

K' 

»o' 

n-' 

ro' 

Cl 
0 

ft. 

II 

// 

// 

// 

1 

11 

+  .78 

2 

+  .90 

23 

+  .35 

—  .04 

3 

7 

+  .54 

3 

+  -47 

10 

+  .42 

+  .25 

5 

10 

+  .C3 

4 

+  .90 

16 

+  .46 

+  .46 

7 

12 

+  .44 

2 

—  .80 

13 

+  .29 

+  .56 

9 

9 

+  .67 

1 

+1.00 

14 

+  -71 

+  .50 

11 

10 

—  .41 

4 

—  .75 

19 

—  .16 

+  .31 

13 

7 

+  .79 

5 

+  .72 

12 

+  .42 

+  .04 

15 

12 

+  .40 

5 

+  .50 

20 

+  .52 

—  .25 

17 

10 

—  .91 

2 

—  .50 

19 

—  .89 

—  .46 

19 

13 

—  .99 

5 

—  .82 

21 

—  .89 

—  .56 

21 

11 

—  .91 

4 

—  .90 

21 

—  .39 

—  .50 

23 

10 

—  .93 

5 

—  .74 

16 

—  .47 

—  .31 

The  values  of  r0'  taken  between  the  limits  —  30°  and  +  90°  of  declination  give 
the  following  correction : — 

-  ".04  +  (".53  ±  ".085)  sin  a  -  (".18  ±  ".085)  cos  a. 

The  formula  reduces  the  sums  of  squares  from  351"  to  312".    With  m  =  10, 

E  =  ±  ".85. 

To  derive  the  final  curve  (order  of  S)  for  use  with  stars  of  Section  X.,  the  resid- 
uals resulting  from  the  definitive  places  of  380  stars  were  first  diminished  by  the  value 
of  the  periodic  term  +  ".53  sin  a  —  ".18  cos  a.  The  result  of  no  star  is  accepted  where 
the  probable  error  of  A  p.'  is  estimated  to  be  greater  than  ".8,  and  where  tbo  same  is 
between  ".G  and  ".8  the  corresponding  residual  is  given  half  weight. 

Never  more  than  5°,  and  generally  not  more  than  4°,  of  declination  were  included 
in  a  single  group.  The  results  follow : — 

Residuals  in  order  of  declination. 


Mean  S 

TT' 

ra" 

Co 

Mean  <! 

rf 

ro" 

Co 

o 

n 

It 

o 

// 

n 

+  86 

7" 

—  .15 

+  .13 

+  21 

25 

—  1.22 

—  1.57 

+  78 

9 

+  .71 

+  .36 

+  16 

19 

—  2.  03 

—  1.62 

+  73 

12 

+  .30 

+  .47 

+  11 

14 

—  1.84 

—  1.40 

+  69 

16 

+  .44 

+  .52 

+  6 

20 

—  .86 

—  1.30 

+  64 

12 

+  .85 

+  .51 

+  1 

12 

—  1.43 

—  1.51 

+  59 

20 

+  .31 

+  .45 

—  5 

5 

—  2.  17 

—  1.86 

+  54 

15 

+  .35 

+  .30 

—  9 

11 

—  2.05 

—  1.94 

+  49 

26 

+  .17 

+  .02 

—  14 

5 

—  2.18 

—  1.85 

+  44 

19 

—  .29 

—  .40 

—  19 

5 

—  .76 

—  1.56 

+  39 

30 

—1.23 

—  .85 

—  23 

5 

—  1.70 

—  1.30 

+  34 

16 

—  1.4U 

—1.04 

—  28 

6 

—  .78 

—  1.11 

+  30 

20 

—  .72 

—1.10 

—  35 

2 

—  .70 

—  1.21 

+  26 

22 

—1.30 

—1.41 

—  42 

5 

—  2.08 

—  1.5 

*  Polaris  is  given  weight  2. 


T99J 


REPORT  OP  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


505 


Of  the  380  stars  employed,  50  received  weight  .5.  The  curve  is  still  very  uncertain. 
From  0°  to  40°  declination  it  is  particularly  unsatisfactory.  By  making  abrupt  changes 
in  the  direction  of  the  curve  at  +  3i>°,  +  30°,  +  15°,  and  +  5°,  the  observations  would 
be  much  better  represented.  I  did  not,  however,  feel  justified  in  taking  this  course. 
The  plus  residuals  from  40°  to  90°  average  much  larger  than  in  the  former  discussion. 
This  appears  to  be  almost  solely  due  to  accidental  causes.  Had  r0"  been  constructed 
without  correction  for  terms  in  a,  the  plus  residuals  would  have  been  reduced  less  than 
one-tenth  of  a  second.  The  probable  error  of  the  unit  of  weight,  using  only  the  329 
residuals  with  weight  1,  north  of  —  30°,  is  i  ".78,  and  considerably  smaller  than  before. 
For  stars  from  +  40°  to  +  90°  it  is  ±  ".88,  +  30°  to  +  40°  ±  1".02,  and  from  —  30°  to 
+  30°  ±  ".66.  I  did  not  think  it  worth  while  to  repeat  the  investigation  of  terms  in  a. 

Bh  1810. 

From  ra  a  preliminary  correction  was  derived  and  used  before  discussing  terms  in 
o.  Column  r0"  is  formed,  taking  into  account  the  effect  of  these  terms.  (70  contains 
values  derived  from  the  definitive  cui*ve. 

Residuals  in  order  of  declination. 


Mean  i 

TT' 

»'o 

ro" 

Co 

0 

// 

// 

// 

86.5 

24 

+  .35 

+  .07 

+  .10 

£   _ 

76.2 

21 

+  .66 

+  .38 

+  .36 

7=2 

70.8 

33 

+  .57 

+  .33 

+  .31 

/ 

66.5 

22 

-  .0* 

+  .25 

+  .19 

60.8 

58 

+  .16 

.00 

+  .01 

56.7 

50 

—  .04 

—  .08 

—  .02 

50.9 

65 

+  .25 

+  .18 

+  .10 

45.6 

55 

+  .03 

+  .08 

+  .10 

40.2 

57 

+  .06 

—  .01 

.00 

The  residuals  are  arranged  in  order  of  a  without  separation  into  zones  of  S.    As 
has  been  stated,  they  result  from  the  use  of  a  preliminary  correction  derived  from 

column  r0. 

Residuals  in  order  of  right  ascension. 


Mean  a 

•K' 

»v 

ft. 

// 

0.99 

49 

—  .10 

3.22 

13 

—  .06 

5.  09 

34 

—  .13 

9.34 

30 

—1.20 

11.78 

48 

—  .30 

14.48 

49 

—  .10 

16.79 

52 

+  .10 

19.63 

73 

+  .73 

22.30 

37 

+  .57 

The  discussion  gives,  in  fair  accordance  with  those  of  Argelander  and  Auwers,  this 
correction : 

-  ".080  ±  ".054  -  (".534  ±  ".077)  sin  a  +  (".404  ±  ".073)  cos  a. 


506          UNITED  STATES  NOETHERN  BOUNDARY  COMMISSION. 

With  m  =  7,  we  have:— 

E  =  ±  1".03.* 


[100J 


Kg  21. 
Within  the  groups  the  variation  in  precision  is  small.    Each  r  is  therefore  given 


weight  1. 


Residuals  in  order  of  declination. 


Mean  t! 

* 

n> 

r, 

+  87.6 

2 

—  .13 

+  .01 

+  76.6 

3 

—  .09 

+  .08 

+  70.8 

4 

+  .37 

+  .12 

+  GO.  9 

7 

+  .03 

+  .18 

+  56.  3 

4 

+  .39 

+  .17 

+  51.1 

7 

-.03. 

+  -14 

+  44.7 

3 

—  .07 

+  .09 

+  40.0 

7 

+  .12 

+  .06 

+  28.1 

4 

+  .29 

+  .06 

+  21.3 

2 

-  .08 

+  .10 

+  14.5 

7 

4-  .07 

+  .13 

+    8.2 

4 

+  .16 

+  -17 

+    4.0 

3 

+  .36 

+  .20 

—    1.1 

1 

+  .44 

+  .27 

—    9.1 

3 

+  .29 

+  .41 

—  14.2 

2 

+  .36 

+  .53 

—  27.6 

2 

+1.25 

+  .84 

With  catalogue  probable  errors  as  an  argument,  and  with  the  probable  error  of 
unit  of  weight  ±  .30,  taking  m  =  4,  we  have  from  the  outstanding  residuals  E  =  ±  .30. 
The  probable  errors  given  in  the  catalogue  are  therefore  adopted  in  the  construction  of 
definitive  weights. 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

—  30°  to  +90° 

—  30°  to  +90° 

Mean  a 

TT' 

ro' 

Mean  a 

ir- 

iV 

II 

n 

1 

6 

+  .15 

13 

3 

—  .03 

3 

3 

—  .13 

15 

8 

—  .26 

5 

7 

—  .21 

17 

8 

—  .08 

7 

1 

+  .10 

19 

8 

—  .17 

9 

2 

-  .05 

21 

8 

+  -14 

11 

5 

+  .26 

23 

4 

+  .08 

'  In  forming  an  opinion  as  to  the  precision  of  the  declination  determinations  of  various  catalogues 
it  is,  of  course,  necessary  to  consider  the  value  of  E  in  connection  with  the  ratio  -.    In  many  cases  the 

value  of  E  does  not  refer  at  all  to  the  probahle  error  of  a  single  observation  ;  and  when  it  can  he  so  con- 
strued, it  is  often  and  necessarily  a  rough  approximation.  The  most  that  can  he  said  is  that  the  adopted 
law  of  probable  errors  for  a  given  catalogue  is  calculated  to  give  with  tolerable  fidelity  the  probable 
errors  due  to  the  numbers  of  observation  most  frequently  occurring  with  the  stars  of  Table  V. 


[101]  BEPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 

Gh22. 


507 


The  use  of  the  correction  zero  adopted  in  Section  VI.  is  continued,  since  no  further 
material  is  available.    The  correction  —  ".11  actually  results. 

Residuals  in  order  of  right  ascension. 


Mean  a 

** 

»o' 

Mean  a 

TT' 

ra' 

1 

3 

// 

—  .06 

13 

1 

II 

—  .10 

3 

1 

—  .70 

15 

4 

+  .10 

5 

4 

+  .08 

17 

3 

-  .12 

7 

1 

.00 

19 

3 

+  .08 

9 

2 

—  .65 

21 

3 

—  .22 

11 

i 

—  .20 

23 

2 

—  .35 

Dt  24. 

The  weights  correspond  to  the  probable  errors  of  the  catalogue,  and  the  unit  of 
weight,  to  a  probable  error  of  ±  ".25. 

Residuals  in  order  of  declination. 


Mean  <J 

JT' 

ro 

Co 

o 

it 

II 

+  86.5 

10 

—  .07 

—  .04 

+  76.3 

11 

—  .04 

—  .16 

+  71.1 

13 

-  .27 

—  .20 

+  66.1 

11 

—  .19 

—  .23 

+  61.4 

16 

—  .32 

—  .25 

+  56.4 

16 

—  .29 

—  .27 

+  50.4 

18 

—  .25 

—  .25 

+  45.2 

12 

—  .23 

—  .22 

+  40.0 

13 

—  .23 

—  .19 

+  32.  1 

3 

—  .74 

—  .14 

+  28.1 

8 

—  .09 

—  .13 

+  21.3 

4 

+  .14 

—  .14 

+  14.6 

14 

—  .19 

—  .22 

+    8.2 

8 

—  .48 

—  .32 

+    4.0 

6 

—  .66 

—  .40 

—    1.1 

2 

—  .50 

—  .51 

—    9.1 

6 

—  .49 

—  .70 

—  14.0 

1 

—  .59 

—  .82 

—  26.1 

2 

—1.32 



Excluding  a  and  S  Ursa?  Minoris,  and  with  m  =  4,  we  have:  — 


The  catalogue  probable  errors  are  adopted. 


508 


UNITED  STATES  NOETHEEN  BOQNDAEY  COMMISSION. 

Residuals  in  order  of  rigJit  ascension. 


[102] 


Declination  limits. 

Declination  limits. 

—  30°  to  +  90° 

—  30°  to  +  90° 

Mean  a 

IT1 

w 

Mean  a 

*•' 

»o' 

1 

13 

II 

—  .06 

13 

16 

// 

+  .02 

3 

7 

+  .06 

15 

24 

+  .10 

5 

17 

—  .10 

17 

19 

—  .53 

7 

2 

+  .;>o 

19 

18 

—  .02 

9 

11 

+  .11 

21 

18 

—  .07 

11 

19 

—  .02 

23 

11 

+  .12 

Va  29. 
Each  r  receives  weight  1. 

Residuals  in  order  of  declination. 


Mean  6 

it 

»0 

Co 

o 

II 

II 

+  74.8 

1 

+  .50 

+  .40 

+  69.9 

1 

+  .81 

+  .40 

+  62.2 

2 

—  .39 

+  .40 

+  55.1 

2 

+  .80 

+  .38 

+  50.3 

3 

+  .61 

+  .31 

+  45.2 

2 

—  .03 

+  .24 

+  38.7 

1 

+  .81 

+  .14 

+  28.1 

4 

—  .19 

-  .08 

+  21.3 

2 

—  .31 

—  .19 

+  14.3 

7 

+  .05 

—  .15 

+    8.2 

4 

—  .14 

—  .13 

+    4.8 

2 

—  .08 

—  .10 

—    1.1 

1 

—  .53 

—  .06 

—    9.1 

3 

—  .13 

—  .01 

No  attempt  is  made  to  discuss  terms  in  a.    With  m  =  4,  we  have: 

E  =  ±  ".47. 


[103] 


EEPOET  OF  THE  CHIEF  ASTEONOMEB,  APPENDIX  E. 

Ao29. 
Residuals  in  order  of  declination. 


509 


Mean  S 

* 

ro 

Co 

o 

II 

„ 

+  88.9 

7 

+  .20 

00 

, 

+  76.6 

33 

+  .00 

00 

^=3 

4-  71.6 

34 

—  .01 

00 

' 

4-  69.3 

33 

+  .02 

00 

4-  61.2 

«0 

—  .05 

00 

4-  56.5 

58 

—  .02 

00 

4-  50.6 

74 

+  .09 

—  .02 

4-  45.0 

77 

—  .13 

—  .07 

+  39.3 

60 

—  .15 

—  .14 

+  34.0 

46 

—  .21 

—  .17 

4-  27.4 

47 

—  .20 

—  .24 

4-  20.9 

43 

—  .30 

—  .28 

+  14.4 

68 

—  .33 

—  .32 

4-  8.4 

41 

—  .32 

—  .38 

+  4.6 

53 

—  .47 

—  .44 

—  1.5 

25 

—  .67 

—  .54 

—  9.1 

27 

—  .58 

—  .66 

—  14.0 

21 

—  .88 

—  .70 

—  18.8 

5 

—  .30 

—  .70 

—  26.  1 

9 

—  .70 

With  m  =  4,  we  have : — 


E  =  ±  ".46. 
Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

—  30°  to  +  90° 

—  30°  to  4-  90° 

Mean  a 

IT' 

r,,' 

Mean  a 

if 

ro' 

h. 

II 

A. 

// 

1 

119 

—  .16 

13 

49 

+  .08 

3 

32 

—  .05 

15 

90 

+  .02 

o 

69 

—  .02 

17 

80 

+  .06 

7 

9 

.00 

19 

88 

—  .09 

9 

71 

+  .34 

21 

98 

+  .07 

11 

79 

.00 

23 

56 

—  .05 

510          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 

Gh  30. 
Each  r  is  given  equal  weight. 

Residuals  in  order  of  declination. 


[104] 


Meau  d 

7T7 

ra 

Co 

o 

it 

*/ 

+  86.3 

6 

+  .55 

+  .11 

-j-  76.7 

5 

—  .18 

+  .15 

+  70.8 

9 

+  .22 

+  .13 

+  66.0 

4 

—  .17 

+  .09 

+  60.8 

15 

—  .05 

+  .03 

+  57.5 

10 

—  .18 

—  .06 

+  50.9 

14 

+  .03 

—  .28 

+  45.7 

12 

—  .47 

—  .50 

+  39.9 

16 

—1.00 

—  .76 

+  33.1 

9 

—1.14 

—1.02 

+  27.2 

11 

—1.29 

—1.19 

+  21.2 

14 

—1.09 

—1.29 

+  14.6 

13 

—  1.51 

—1.31 

+    9.0 

19 

—1.36 

-1.81 

+    4.1 

9 

—1.11 

—1.34 

—    1.8 

12 

—1.51 

—1.41 

—    8.5 

10 

—1.28 

—1.62 

—  14.  1 

4 

—2.00 

—1.91 

—  18.7 

3 

—2.  10 

—2.36 

—  22.4 

4 

—2.75 

—  2.C7 

—  27.9 

4 

—2.9 

—2.9 

—  34.1 

1 

+9.3 

r   * 

With  m  =  5,  we  have: — 


E  =  ±  ".33. 
Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +5° 

+  40°  to—  30° 

—  30°  to  +90° 

Mean  a 

7T7 

r0' 

V 

»•„' 

K* 

'V 

h. 

n 

// 

// 

1 

2 

—  .25 

11 

+  .15 

21 

+  .20 

3 

3 

+  .43 

7 

+  .24 

10 

+  .16 

5 

4 

+  .57 

10 

+  .12 

16 

—  .04 

7 

2 

+  .50 

12 

+  .13 

13 

+  .33 

9 

1 

—  .30 

9 

—  .16 

13 

+  .06 

11 

4 

—  .10 

10 

—  .14 

19 

—  .07 

13 

5 

+  .12 

7 

+  .09 

13 

.00 

15 

5 

+  .32 

12 

+  .03 

20 

—  .04 

17 

2 

—  .80 

10 

—  .45 

20 

—  .35 

19 

5 

—  .06 

13 

—  .15 

21 

—  .03 

21 

4 

—  .17 

10 

—  .18 

20 

—  .16 

23 

5 

+  .30 

9 

+  .17 

14 

+  .08 

A  small  correction,  depending  on  the  right  ascension,  may  be  indicated, 
discussion  was  not,  however,  undertaken. 


The 


[105]  EEPOET  OP  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  51 1 


C.  G.  H.  31. 
Residuals  in  order  of  declination. 


Mean  <5 

TT' 

r<> 

Co 

o 

H 

n 

+  12.7 

2 

—  .88 

+  .35 

e 

+    8.2 

9 

+  .00 

+  .35 

r=2- 

+    3.3 

3 

+  .61 

+  .35 

/ 

—    0.7 
—    8.4 
—  17.9 

7 
11 
2 

+  .55 
+  .27 
+1.0-2 

+  .35 
+  .35 
+  .35 

For  (he  last  five  groups 
the  weights  are  estimated. 

—  21.1 

4 

—  .60 

+  .35 

—  26.5 

3 

+  .61 

+  .35 

—  35.0 

2 

+1.08 

+  .17 

—  41.4 

2 

—  .51 

+  .03 

—  52.6 

1 

+  .38 

.00 

—  r>9.9 

5 

—  .40 

.00 

—  78.1 

1 

+  .90 

.00 

The  correction  is  extremely  uncertain,  owing  to  the  small  number  of  observations, 
as  well  as  large  probable  error.  The  value  of  E  is  estimated  to  be  ±  1".2. 

The  declinations  have  not  been  employed  in  the  reduction  of  any  stars  between  the 
limits  of  declination  +  90°  and  —  30.° 

S.  H.  31. 

The  values  of  r  are  applicable  to  the  catalogue  places  as  reduced  with  Young's 
refractions. 

Residuals  in  order  of  declination. 


Mean  3 

* 

,o 

Co 

o 

II 

„ 

+  73.1 

15 

+  1.0 

+  1.30 

e 

+  65.1 

4 

+    .1 

+  1.30 

—  =2 

+  62.4 

10 

+  1.37 

+  1.30 

' 

+  56.2 

11 

+  1.20 

+     .30 

+  51.0 

19 

+  1.76 

+     .30 

+  44.7 

7 

+  1.20 

+     .30 

+  38.7 

8 

+    .90 

+     .30 

+  33.2 

6 

+  1.21 

+     .30 

+  27.9 

33 

+  1.18 

+     .30 

+  21.  3 

18 

+  1.85 

+     .30 

+  14.6 

53 

+  1.26 

+  1.30 

+    82 

35 

+  l.CO 

+  1.26 

+    4.1 

24 

+  1.35 

+  1.21 

—    2.4 

55 

+     .79 

+  1.13 

—    8.5 

70 

+  1.2-2 

+  1.00 

•  —  14.  1 

30 

+  1.32 

+    .86 

—  18.5 

18 

+    .24 

+    -74 

—  23.9 

17 

—  1.09 

+    .65 

—  2H.1 

31 

+    .71 

+     .61 

—  35.0 

2 

—    .13 

+     .60 

—  42.1 

5 

+    .69 

+    .60 

—  50.4 

2 

+  1.41 

+    .60 

—  59.2 

6 

+    .66 

+     .41 

—  74.8 

3 

+    .14 

+     .35 

512 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[106] 


There  appears  to  be  a  well-marked  correction  depending  on  a,  as  is  shown  in  the 
following  table: — 

Residuals  in  order  of  right  ascension. 


Declination  limits. 
—  30°  to  +5° 

Declination  limits. 
+  5°  to  +60° 

Declinatiou  limits. 
—  30°  to  +60° 

Mean  a 

n' 

ro' 

Mean  a 

7r' 

»o' 

Mean  « 

TT' 

ft' 

ft. 

1.0 
3.3 
5.8 
7.4 
9.3 
11.2 
13.0 
15.6 
18.9 
21.8 

16 
16 
25 
14 
9 
7 
22 
44 
28 
56 

II 

+  .25 
+  .73 
+  .26 
—  .89 
—  .10 
4-  .50 

ft. 
23.8 
2.5 
5.2 
7.6 
11.2 

29 
16 
18 
9 
24 

// 

+  .58 
+  .98 
+  .30 
+  .10 
—  .75 

h. 
0.7 
3.6 
5.7 
8.3 
11.3 
13.2 
15.5 
18.2 
19.9 
22.3 

46 
32 
42 
24 
31 
31 
69 
52 
56 
52 

a 

+  .46 
+  .86 
+  .02 
—  .25 
—  .46 
—  .10 
—  .66 
—  .23 
—  .16 
+  .38 

—  .39 
—  .61 

—  .28 
+  .18 

14.9 

18.0 
19.9 

34 
36 
32 

-  .38 
—  .12 
—  .10 

rn'  in  limits  —  30°  to  +  60°  gives  the  correction  +  ".27  sin  «  +  ".47  cos  a.    The 
probable  error  of  each  coefficient  is  ±  ".09. 
With  TO  =  6,  we  have : — 

E  =  ±  l".34. 

C.  G.  H.  33. 
Each  r  is  given  weight  1. 

Residuals  in  order  of  declination. 


Mean  i 

ff' 

n> 

Co 

o 

n 

// 

+  33.2 

1 

+  .35 

+  .31 

+  27.7 

7 

+  -41 

+  .54 

+  21.7 

7 

+  .69 

+  .48 

+  14.2 

8 

—  .25 

+  -11 

+    8.4 

7 

—  .22 

—  .09 

+    3.7 

6 

+   .29 

—  .14 

—    2.2 

5 

—  .16 

—  .10 

—    8.6 

6 

—  .02 

+  .10 

—  14.1 

4 

+  .32 

+  .40 

—  18.7 

3 

+  .70 

+  .65 

—  22.4 

4 

+1.05 

+  .79 

—  27.9 

4 

+  .92 

+  .89 

—  35.0 

2 

+  1.15 

+  -71 

—  4i  1 

5 

+  .04 

+  .32 

—  55.  1 

2 

—  .60 

+  .05 

—  59.2 

7 

+  .04 

+  .01 

—  75.1 

3 

—  .11 

—  .09 

With  m  =  6,  we  have: — 


E  =  +  ".30. 


[1071 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 

Residuals  in  order  of  right  ascension. 


513 


Declination  limits. 

Declination  limits. 

+  40°  to  —  30° 

+  40o  to—  30° 

Mean  a 

TT' 

n,' 

Mean  a 

•K" 

ro' 

ft. 

/; 

h. 

// 

0.35 

5 

+  .10 

13.40 

4 

+  .25 

3.00 

5 

—  .12 

15.53 

9 

+  .02 

5.41 

8 

+  .19 

18.31 

7 

+  .09 

7.  66 

5 

—  .34 

19.72 

5 

—  .04 

10.67 

7 

+  .09 

22.06 

7 

—  .33 

Ce  34. 

Residuals  in  order  of  declination. 


Mean  6 

* 

ro 

Co 

o 

It 

„ 

+  87.3 

25 

—  .08 

.00 

€     n 

+  75.5 

14 

+  .06 

—  .04 

_=3 

e 

•  +  69.7 

14 

—  .25 

—  .14 

+  66.2 

17 

—  .18 

—  .24 

+  61.2 

31 

—  .59 

—  .38 

+  56.6 

43 

—  .28 

—  .52 

+  50.3 

23 

—  .71 

—  .70 

+  45.0 

21 

—  .87 

—  .78 

+  -59  4 

15 

—  .79 

—  .83 

+  33.2 

8 

—  .57 

—  .82 

+  27.  8 

48 

—  .83 

—  .86 

+  20.4 

50 

—  .46 

—  .56 

+  14.3 

52 

—  .47 

—  .39 

+  8.5 

67 

—  .25 

—  .36 

+  4.1 

24 

—  .46 

—  .40 

—  0.8 

22 

—  .19 

—  .49 

—  8.4 

36 

—  .85 

—  .70 

—  14.0 

12 

—1.22 

—  .85 

—  19.2 

10 

—  .62 

—  .96 

—  21.7 

9 

—  .79 

—  .99 

—  2H.  4 

13 

—1.25 

—1.00 

—  34.  1 

o 

—1.4 

With  m  =  5,  we  have: — 


E  ±  ".70. 


B 33 


514 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 

Residuals  in  order  of  right  ascension. 


[WSJ 


Declination  limits. 

Declination  limits. 

Declination  limits. 

Declination  limits 

+  40°  to  —  30° 

+  40°  to  +  90° 

—  30°  to  +  5° 

—  30°  to  +  90° 

Mean  a 

tr1 

re' 

ir' 

ro' 

*> 

)•„' 

tf 

>•„' 

h. 

// 

// 

// 

// 

1 

•   35 

+  .16 

32 

—  .23 

3 

—  .70 

67 

—  .01 

3 

22 

+  .58 

10 

—  .44 

8 

+  .30 

32 

+  .26 

5 

31 

—  .21 

11 

—  .35 

5 

—  .20 

4J 

—  .25 

7 

24 

+  .04 

24 

-t-    04 

9 

l!2 

+  .39 

5 

—  .50 

8 

+  .40 

27 

r  •    ^* 
+  .23 

11 

32 

+  .03 

34 

+  .14 

8 

+  .05 

66 

+  .09 

13 

26 

+  .11 

25 

+  .23 

20 

+  .20 

51 

+  -17 

15 

50 

—  .06 

9 

+  .20 

14 

+  .42 

59 

—  .02 

17 

22 

-h  .03 

9 

+  .12 

7 

+  .48 

31 

+  .06 

19 

49 

—  .13 

17 

—  .05 

7 

—  .54 

66 

—  .11 

21 

25 

—  .12 

33 

+  .10 

25 

—  .12 

58 

.00 

23 

21 

—  .45 

7 

—  .06 

4 

—  .25 

28 

—  .35 

No  certain  correction  following  a  appears  to  be  indicated. 

Mb  34. 

In  Observations  Astronomical,  1833  and  1834,  Laniont  compares  his  declinations  of 
fundamental  stars  with  those  of  Bessel  and  Struve.  The  comparisons  are  used  in 
finding  the  curve  of  correction,  but  no  use  is  made  of  the  declinations  of  the  stars  so 
compared. 

Eesiduals  in  order  of  declination. 


Mean  d 

ir1 

»'o 

<"o 

o 

// 

II 

+  74.4 

12 

—  .29 

—  .29 

e  3 

+  62.6 

14 

—  .36 

—  .49 

e. 

+  57.6 

7 

—  .68 

—  .56 

/ 

+  49.6 

27 

—  .74 

—  .62 

+  40.1 

36 

—  .55 

—  .54 

+  32.0 

15 

—  .28 

—  .24 

+  27.7 

50 

+  .01 

+  .01 

+  21.0 

66 

+  .27 

+  .29 

+  14.6 

72 

+  .43 

+  .47 

+  9.1 

79 

+  .63 

+  .50 

+  4.3 

42 

+  .94 

+  .49 

—  1.5 

49 

—  .14 

+  .38 

—  9.0 

43 

+  .53 

+  -I? 

—  14.2 

19 

+  .70 

—  .01 

—  19.7 

9 

—  .43 

—  .19 

—  26.2 

20 

—  .61 

—  .5 

[109J 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  515 


Inadvertently  the  nutation  correction  was  not  applied  to  the  values  of  r  previous 
to  the  above  discussion.    The  outstanding  residuals  are: — 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  25°  to  +5° 

+  5c>to+75° 

+  75°  to  —  25C 

Mean  a 

TT' 

n,' 

J 

'•o' 

7T7 

n>' 

J>. 

// 

// 

n 

I 

2 

+  1.70 

42 

+  .-19 

44 

+  .51! 

3 

10 

+     .82 

9 

+  .01 

19 

+  .44 

5 

17 

—    .11 

28 

+  .11 

45 

+  .03 

7 

4 

—  1.50 

45 

—  .32 

49 

-  .42 

9 

19 

+    .10 

28 

+  .16 

37 

+  -14 

11 

20 

—    .45 

55 

—  .40 

75 

—  .41 

13 

20 

—    .04 

7 

—  .03 

27 

—  .04 

15 

17 

+     .34 

55 

+  -17 

72 

+  .21 

17 

4 

—    .40 

44 

—  .17 

48 

—  .19 

19 

13 

+     .05 

31 

+  .22 

44 

+  -17 

21 

Id 

-    .07 

20 

+  -17 

38 

+  .06 

23 

19 

+     -41 

11 

+  .63 

30 

+  .49 

Discussed  for  terms  in  a,  the  last  column  (+  75°  to  —25°)  gives: 

+  ".03  sin  a  +  ".27  cos  a, 

which  agrees  well  with  the  nutation  correction  +  ".02  siu  «  +  .18  cos  «.    The  latter  is 
therefore  adopted. 

With  TO  =  5,  we  have : — 

E  =  ±  1".05. 

Eh  37. 
Residuals  in  order  of  declination. 


Menu  (J 

TT' 

ID 

Co 

o 

// 

// 

+  86.9 

24 

—  .18 

—  .21 

£ 

+  76.6 

15 

—  .37 

—  .23 

_  y 

+  70.4 

7 

—  .18 

—  .23 

Kl 

+  66.3 

6 

—  .66 

—  .22 

+  61.4 

26 

—  .14 

—  .21 

+  56.0 

21 

—  .18 

—  .18 

+  50.8 

30 

—  .22 

—  .16 

+  45.  4 

16 

+  .01 

—  .15 

+  39.3 

16 

—  .10 

—  .16 

+  33.5 

10 

—  .43 

—  .18 

+  27.6 

36 

—  .15 

—  .20 

+  21.2 

45 

-  .31 

-.18 

+  14.5 

46 

—  .25 

—  .04 

+  9.0 

56 

+  .31 

+  .03 

+  3.9 

27 

+  .07 

—  .03 

—  1.3 

29 

—  .24 

—  .17 

—  8.6 

32 

—  .51 

—  .26 

—  14.1 

15 

—  .23 

—  .26 

—  18.7 

9 

—  .25 

—  .18 

—  21.9 

9 

+  .80 

-  .09 

—  28.6 

7 

+  .44 

+  .2 

With  m  =  8,  we  have: — 


=±  ".52. 


516          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.         [110 1 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +5° 

+  5°  to  +40° 

+  40°  to  +90° 

—  30°  to  +90° 

Mean  a 

TT' 

'•o' 

V? 

Itf 

7T7 

ro' 

TT' 

V 

h. 

// 

// 

II 

// 

1 

C 

—1.05 

26 

+  -14 

15 

4-  .16 

47 

.00 

3 

10 

4-  .25 

10 

+  .08 

5 

—  .04 

25 

+  -12 

5 

14 

+  .16 

20 

—  .56 

12 

+  .30 

46 

—  .11 

7 

24 

•4-  .08 

5 

—  .02 

29 

4-     06 

9 

4 

+  .20 

18 

n   •  **** 

—  .17 

11 

+  -14 

33 

~      .    V\J 

—  .02 

11 

13 

+  .02 

20 

+  .11 

16 

-  .05 

49 

4-  .03 

13 

15 

+  .19 

8 

—  .15 

10 

.00 

33 

+  .03 

15 

14 

4-  .66 

18 

—  .43 

9 

—  .3-2 

41 

+  .34 

17 

G 

—  .15 

11 

-  .04 

19 

.00 

36 

—  ..01 

19 

7 

—  .42 

27 

—  .01 

7 

+  -11 

41 

—  .06 

21 

15 

—  .23 

17 

+  .09 

23 

—  .11 

55 

—  .08 

23 

13 

—  .31 

18 

+  .21 

10 

—  .06 

41 

—  .02 

A  correction  is  indicated,  such  as  might  be  due  to  an  error  in  the  adopted  temper- 
ature coefficient  in  refraction.  Very  little  correction  is  shown  in  the  summary.  I  have 
thought  it  safest  to  neglect  the  discussion  of  terms  in  a.  (Tide  Eh  43). 

Kg  38. 

Each  r  was  given  equal  weight.    The  numbers  in  column  ra"  result  from  a  redis 
cussion  adopting  the  value  of  the  periodic  formula  deduced  below  for  terms  in  «. 

Residuals  in  order  of  declination. 


Mean  <! 

rf 

'•o 

Co 

n>" 

o 

// 

// 

II 

4-87.5 

2 

—    .05 

-    .05 

—    .07 

+  75.8 

2 

—    .21 

—    .26 

—    .11 

+  71.2 

2 

—    .75 

—    .32 

—     .54 

+  62.2 

2 

—    .69 

—    .24 

—     .60 

4-  55.1 

2 

4-    .44 

4-    .10 

4-    .40 

+  51.1 

7 

4-     .65 

4-     .24 

+    .84 

+  45.9 

8 

4-  1.03 

4-    .30 

4-    .80 

+  39.8 

6 

—    .08 

4-     .22 

—    .01 

+  28.1 

4 

—    .07 

4-    .08 

—    .17 

+  21.3 

2 

—    .01 

+     .13 

—    .01 

-f-  14.3 

7 

4-    .39 

4-     .27 

+     .42 

4-    8.2 

4 

4-    .29 

4-     .46 

4-     .41 

4-4.0 

3 

4-  1.10 

4-    .59 

4-  1.10 

—    1.1 

1 

4-  1.10 

4-     -77 

4-  1.05 

—    9.1 

3 

4-    .99 

4-  1.09 

4-     .97 

—  14.2 

2 

4-  1.36 

4-  1.31 

4-  1.62 

—  26.1 

1 

4-  2.8 

+  1.8 

4-  3.16 

The  declination  curve  founded  on  r0  is  adopted. 


[Ill]  EEPOET  OF  THE  CHIEF  ASTBONOMEE,  APPENDIX  H.  517 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

—  30°  to  +90° 

—  30°  to  +90° 

Mean  <! 

*> 

rj 

Mean  6 

TT7 

1%' 

k. 

II 

h. 

// 

0.9 

6 

+  .27 

13.3 

2 

—  .45 

3.1 

4 

+  .75 

14.9 

7 

—  .44 

5.2 

5 

+  .50 

17.1 

5 

+  .42 

7.0 

1 

+  .20 

19.3 

8 

+  .13 

9.7 

9 

—  .05 

20.9 

5 

+  .04 

11.5 

4 

—  .30 

23.3 

2 

+  .15 

The  correction  depending  on  a  is  quite  marked.  The  result  is  +  ".14  +  ".24  sin 
a  +  ".32  cos  a.  The  probable  errors  of  the  terms  in  a  are  each  ±  .07.  The  formula 
of  correction  is  adopted. 

With  m  =  8,  we  have : — 

E  =  ±  ".39. 

Gh  39. 
Residuals  in  order  of  declination. 


Mean  <5 

ff' 

* 

,C0 

o 
+  86.5 

79 

II 

+  .or 

It 

+  .01 

£ 

+  76.7 

71 

+  .05 

+  .04 

__4 

+  70.5 

67 

+  .10 

+  .08 

' 

+  66.2 

62 

—  .10 

+  .09 

+  60.9 

176 

+  .06 

+  .10 

+  56.8 

147 

+  .07 

+  .11 

+  50.9 

138 

+  .20 

+  .12 

+  45.5 

136 

+  .02 

+  .12 

+  39.7 

98 

+  .07 

+  .13 

+  32.  9 

54 

+  .22* 

+  .14 

+  27.4 

114 

+  .19 

+  .16 

+  21.1 

134 

+  .15 

+  .19 

+  14.5 

130 

+  .26 

+  .24 

+    8.9 

135 

+  .29 

+  .29 

+    3.9 

85 

+  .37 

+  .35 

—    1.6 

90 

+  .40 

+  .43 

—    8.6 

97 

+  .53 

+  .56 

—  14.1 

51 

+  .71 

+  .68 

—  18.7 

36 

+  .53 

+  .80 

—  22.5 

44 

+1.04 

+  .90 

—  28.1 

44 

+1.24 

+1.05 

With  m  =  4,  we  ha.ve : — 


518 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 

Residuals  in  order  of  right  ascension. 


[112] 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +5° 

+  4Qo  to  _  3Qo 

—  30°  to  +900 

Mean  a 

TT' 

r«' 

TT' 

'•./ 

TT' 

'•o' 

h. 

// 

// 

// 

1 

25 

—  .21 

96 

—  .15 

212 

—  .13 

3 

39 

—  .13 

57 

—  .24 

95 

—  .13 

5 

48 

—  .41 

107 

—  .20 

174 

—  .18 

7 

25 

+  .31 

89 

+  .H 

103 

+  .10 

9 

13 

—  .30 

73 

—  .11 

127 

—  .11 

11 

33 

+  .01 

89 

+  .13 

207 

+  .13 

13 

48 

+  .17 

74 

+  .08 

152 

+  .09 

15 

45 

+  .H 

108 

+  .20 

202 

+  .12 

17 

25 

—  .04 

72 

+  .09 

168 

+  .05 

19 

20 

+  .20 

119 

—  .C7 

201 

+  .05 

21 

45 

+  .27 

89 

—  .21 

212 

—  .06 

23 

36 

—  .13 

84 

—  .10 

144 

—  .11 

A  tolerably  well-marked  correction  depending  on  a  is  indicated.     No  discussion  is 
undertaken,  however,  as  the  correction  would  in  any  case  be  very  small. 

Ce  40. 

The  weights  formed  in  the  manner  explained  in  Section  V.  evidently  increase  too 
rapidly  with  the  number  of  observations. 

Residuals  in  order  of  declination. 


Meon  i 

7T 

»'o 

Co 

•K'  is  therefore  formed 

in  this  manner  : 

o 

// 

+  86.6 

75 

+  .02 

.00 

Weight  com- 

+ 76.6 

55 

+  .12 

.00 

puted    ac- 

«r* 

+  70.2 

33 

—  .11 

—  .07 

cording  to 

71 

+  65.8 

34 

—  .08 

—  .16 

Section  V. 

+  61.2 

134 

—  .38 

—  .29 

+  56.2 

65 

—  .37 

—  .40 

+  49.6 

57 

—  .54 

—  .55 

1  to  5 

1  to  5 

+  45.3 

91 

—  .62 

—  .65 

6 

6 

+  39.0 

74 

—  .75' 

—  .77 

7 

6 

+  32.9 

24 

—  .83 

—  .85 

8  and  9 

7 

+  27.7 

85 

—  .83 

—  .89 

10  and  11 

8 

+  21.2 

113 

—  .78 

—  .82 

12  to  14 

9 

+  14.4 

118 

—  .57 

—  .58 

15  to  17 

10 

+    8.9 

116 

—  .37 

—  .47 

18  to  21 

11 

+    3.7 

56 

—  .51 

—  .54 

22  to  25 

12 

—    1.3 

57 

—  .78 

—  .64 

26  to  30 

13 

—    8.6 

70 

—  .65 

—  .70 

31  to  35 

14 

—  14.1 

25 

—  .93 

—  .68 

36  to  40 

15 

—  19.4 

11 

—  .35 

—  .56 

41  to  46 

16 

—  21.9 

8 

—  .43 

—  .50 

47  to  52 

17 

—  26.3 

7 

—  .07 

—  .4 

53  to  58 

18 

59  to  65 

19 

66  to  72 

20 

73  to  80 

21 

81  to  88 

22 

89  to  96 

23 

97  to  105 

24 

106,  or  more 

25 

[1131  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          519 

• 

Residuals  in  order  of  right  ascension. 


Declination  limits. 
—  30°  to  +  5° 

Declination  limits. 
+  50  to  +  40° 

Declination  limits. 
+  4Qo  to  —  30° 

Declination  limits. 
+  40°  to  +  90° 

Declination  limits. 
—  30°  to  +  90° 

Mean  o 

vr' 

ro' 

V 

nt 

sr' 

ro' 

TT' 

ra' 

71"' 

*t 

h. 
I 
3 
5 
7 
9 
11 
13 
15 
17 
19 
21 
23 

6 
20 
16 

// 

+  .45 
+  .16 
+  .23 

62 
13 
43 
54 
44 
48 
24 
63 
42 
86 
32 
30 

ii 

—  .09 
—  .15 
+  .09 
+  .26 
+  .34 
+  .04 
—  .03 
+  .14 
—  .02 
—  .04 
—  .19 
—  .28 

68 
33 
59 
54 
53 
61 
44 
92 
52 
100 
73 
54 

// 

—  .04 
+  .04 
+  .13 
+  .26 
+  .35 
+  .12 
+  .05 
+  .10 
—  .01 
—  .04 
—  .25 
—  .21 

79 
30 
44 

II 

+  .06 
—  .07 
—  .11 

147 
63 
103 
54 
85 
139 
90 
138 
97 
150 
149 
86 

II 

+  .01 
—  .01 
+  .03 
+  .26 

+  .U 
—  .02 
+  .12 
+  .06 
—  .01 
—  .07 
—  .12 
—  .04 

9 
13 
20 
29 
10 
14 
41 
24 

+  .40 
+  .39 
+  .14 
+  .02 
+  .06 
—  .06 
—  .30 
—  .13 

32 
78 
46 
46 
45 
GO 
76 
32 

—  .28 
—  .12 
+  .19 
—  .02 
—  .02 
—  .11 
+  .01 
+  .25 

A  correction  varying  with  the  right  ascension  is  well  marked  in  the  zone  +  40° 
to  —  30°  (and  is  supported  in  some  degree  by  Ce  34).  I  find  -f  (".15  ±  .025)  sin  a  — 
(".15  ±  .025)  cos  a. 

With  TO  =  8,  we  have : — 

E=±  ".46,  Ce  48  gives  ±  ".62,  and  Ce  56  ±  ".60.    I  have  adopted  H  =  ±  60. 

Ah  41  and  Ah  52. 

These  were  at  first  treated  as  separate  catalogues,  but  the  experiment  proved  that 
there  exists  between  them  no  difference,  which  can  be  safely  predicated  from  the 
material.  Ooms's  very  thorough  comparison  of  Robinson's  Armagh  Catalogue  (Ast, 
Nach.  Bd.  59,  p.  248),  after  the  proper  correction,  has  been  relied  upon  to  a  great  extent 
in  drawing  the  curve. 


520          UNITED  STATES  NORTHERN   BOUNDARY  COMMISSION.         [114] 

Residuals  in  order  of  declination. 


Direct  comparison. 

Through  Ao  29. 

Difference 

Mean  i 

w7 

ra 

Co 

Mean  i 

Number  of 

stare. 

uncorrectcd, 
applicable  to 
Armagh  dec- 

Difference 
corrected. 

lination. 

o 

it 

it 

o 

// 

// 

+  76.2 

11 

+    .21 

+    .20 

+  81.2 

4 

+    .52 

+    .88 

+  71.2 

20 

+    .05 

+    .20 

+  77.1 

6 

+    .23 

+    .56 

+  66.4 

17 

—    .06 

+    .20 

+  72.4 

8 

+    .34 

+    .63 

+  61.0 

3d 

+    .11 

+    -17 

+  66.7 

8 

—    .39 

-    .16 

+  56.5 

32 

+    .08 

+     .05 

+  62.  4 

11 

+    .38 

+    .56 

+  51.4 

38 

+    .07 

—    .10 

+  57.5 

15 

—    .35 

—    .23 

+  45.5 

46 

—  1.13 

—     .71 

+  51.6 

15 

—    .31 

—    .27 

+  40.1 

49 

—    .40 

—    .81 

+  47.5 

15 

—    .69 

—    .75 

+  32.9 

20 

—    .66 

—    .54 

+  42.9 

22 

—    .85 

—  1.02 

+  26.  5 

24 

—    .20 

—    .30 

+  37.5 

32 

—    .18 

—    .49 

+  21.0 

25 

—    .16 

—    .27 

+  32.7 

17 

—    .10 

—    .52 

+  15.1 

16 

—    .83 

—    .47 

+  27.4 

29 

+    .04 

—    .47 

+    9.3 

41 

—    .61 

—    .78 

+  22.3 

23 

+    .41 

—    .18 

+    3.7 

15 

—    .24 

—  1.08 

+  17.7 

31 

+    .30 

—    .36 

-    1.7 

22 

—  1.14 

—  1.21 

+  12.4 

18 

+    .08 

—    .56 

—    8.2 

14 

—    .54 

—  1.  15 

+    7.6 

22 

—    .45 

—  1.05 

+    3.0 

31 

—    .46 

—  1.07 

—    2.5 

—    7.7 

17 
14 

—  1.21 

+    .38 

—  1.98 
—    .58 

it1  is  formed  with  —  =  2. 

e; 

—  13.1 
—  16.8 

19 
24 

—    .21 

+    .58 

—  1.24 
—    .47 

—  23.6 

2 

—  2.05 

—  3.0 

With  TO  =  6,  we  have: — 


E  =  ±  I'M. 


Residuals  in  order  of  right  ascension. 


Mean  a 

^ 

ro' 

Mean  a 

TT' 

r«' 

h. 

tt 

ft. 

// 

1 

48 

—  .03 

13 

27 

—  .16 

3 

19 

+  .05 

15 

40 

+  .05 

5 

33 

—  .34 

17 

35 

—  .37 

7 

20 

—  .02 

19 

35 

+  .18 

9 

34 

+  .64 

21 

48 

+  .01 

11 

59 

+  .03 

23 

38 

+  .26 

[115]  EEPOET  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          521 


Kg  43. 

The  correction  in  order  of  declination  is  adopted  as  it  results  from  the  discussion 
in  Section  VI.  (Table  II.).  In  the  following  table,  each  value  of  r1  is  supposed  to  have 
an  equal  degree  of  precision. 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

—  30°  to  +  42° 

—  30°  to  +42° 

Mean  a 

ff7 

rj 

Mean  a 

7T1 

r0' 

ft. 

n 

A. 

,1 

0.7 

3 

—  .40 

13.3 

1 

—  .20 

2.9 

1 

—  .40 

15.0 

4 

—  .12 

5.4 

5 

+  .14 

17.0 

3 

+  .10 

7.6 

1 

-  .30 

19.4 

4 

+  .40 

9.7 

2 

—  .20 

20.9 

3 

+  .40 

11.7 

1 

—  .30 

22.9 

1 

+  .20 

The  division  into  two  zones,  which  was  made,  is  of  no  interest,  owing  to  the  small 
number  of  stars.    From  the  above  is  found  as  a  correction : — 

—  (".16  ±  ".06)  sin  a  +  (".13  ±  ".07)  cos  a ; 

and  this  is  adopted. 

Dr.  Auwers  found  (Ast.  Nach.,  Bd  65,  S.  230)  :— 

—  ".139  sin  (a  —  25°  38')  —  ".239  (sin  2  a  +  05°  270- 

The  term  depending  on  2  a  is  indeed  indicated,  but  I  have  preferred  to  neglect  it, 
since  the  number  of  residuals  is  small. 
With  m  =  4,  we  have : — 

E  =  ±  ".26. 


522 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[1161 


Eh  43. 

Residuals  in  order  of  declination. 


Mean  6 

v1 

ro 

Co 

o 

it 

// 

+  86.8 

156 

+  .06 

.00 

The  weights  (TT')  are 

+  76.5 

85 

+  -14 

.00 

constructed    according 

+  70.5 

24 

—  .44 

.00 

to    Section  V.,    which 

+  66.5 

7 

—  .20 

—  .01 

supposes  : 

+  61.3 

33 

—  .08  . 

—  .04 

f 

+  56.5 

54 

—  .14 

—  .07 

_  o 

+  50.6 
+  45.5 

54 

38 

+  .07 
—  .19 

—  .08 
—  .06 

The  argu  raent  for  form- 
ing n1  is  not  therefore 

+  39.4 

42 

-f  .03 

—  .03 

the  total  cumber  of  ob- 

+ 33.3 

18 

+  .33 

+  .02 

servations,  but  the  sum 

+  27.4 

66 

+  .14 

+  .09 

of  the  values  of  ir1  in 

+  21.3 

66 

—  .10 

+  .17 

each  year. 

+  14.2 

68 

+  .18 

+  .28 

+    8.6 

66 

+  .40 

+  .35 

+    4.1 

42 

+  .10 

+  .36 

—    1.4 

52 

+  .40 

+  .31 

—    8.7 

65 

+  .26 

+  .16 

—  14.1 

31 

—  .07 

+  .04 

—  18.8 

21 

—  .50 

-  .06 

—  22.  0 

17 

—  .38 

—  .12 

—  27.0 

10 

+  .0 

—  .02 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Decl  i  nation  limits. 

DeclinatioB  limits. 

Declination  limits. 

—  30°  to  +  5° 

+  5°  to  +  40° 

+  40°  to  —  30° 

-j.  4QO  to  +  90° 

—  30°  to  +  90° 

Mean  a 

*> 

n>' 

It1 

nf 

7T7 

«•„' 

*-' 

n>' 

*> 

ro' 

h. 

li 

li 

// 

n 

// 

1 

15 

—  .54 

40 

—  .35 

55 

—  .40 

75 

—   .11 

130 

—  .24 

3 

19 

—  .40 

6 

—  .10 

25 

—  .54 

15 

—  .13 

40 

.  .    ;jf) 

5 

30 

+  .01 

24 

+  -12 

54 

+  .61 

21 

+  .04 

75 

+  .'05 

7 

6 

+  .50 

40 

+  .03 

46 

+  .09 

24 

.00 

70 

+  .06 

9 

9 

+  .60 

37 

+  .09 

46 

+  .19 

14 

+  .23 

60 

+  .20 

11 

16 

—  .yj 

25 

+  .20 

41 

—  .03 

37 

+  .05 

78 

+  .01 

13 

14 

—  .30 

17 

+  .64 

31 

+  .22 

31 

+  .06 

62 

+  .14 

15 

28 

—  .07 

36 

+  .24 

64 

+  .10 

63 

+  .30 

127 

+  .20 

17 

12 

—  .05 

27 

+  .02 

39 

-  .01 

54 

+  .22 

93 

+  .13 

19 

21 

+  .14 

42 

—  .07 

63 

.00 

43 

+  .06 

106 

+  .02 

21 

33 

—  .08 

20 

—  .15 

53 

—  .11 

57 

—  .09 

110 

-  .10 

23 

20 

+  .03 

W 

—  .22 

38 

—  .09 

31 

—  .27 

69 

—  .  17 

A  correction  depending  on  a  is  quite  well  marked  in  all  the  zones.    The  discussion 

gives : — 

—  (".05  ±  ".03)  sin  a  —  (".19  ±  ".03)  cos  a. 

Dr.  Auwera  found  (Ast.  Nacli.,  Bd  64,  8.  343)  -  ".002  sin  a  —  ".310  cos  a  for  the 
Edinburgh  declinations,  1835-1839,  assuming  Ao  29  and  Gh  1755  to  require  no  correc- 
tion. This  corresponds  tolerably  well  with  Eh  37,  between  the  declination  limits  —  30° 


[117]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  523 


to  +  5°,  as  exhibited  above.  Later  (Ast.  Nach.,  Bd  65,  p.  227),  Dr.  Auwers  finds  that 
two-thirds  of  the  correction  best  corresponds  with  residuals  derived  from  his  discussion 
of  fundamental  stars.  This  accords  almost  perfectly  with  the  formula  given  above  for 
Eh  43.  But  Dr.  Auwers  supposes  this  formula  not  to  be  applicable  to  the  later  obser- 
vations of  Henderson. 

With  m  =  8,  we  have : — 

E  =  ±  ".67. 

±  ".66  results  from  the  discussion  in  Section  V.     The  former  is  adopted. 

,Gh  45. 
Residuals  in  order  of  declination. 


Mean  <! 

•x' 

,o 

Co 

o 

„ 

„ 

+  86.8 

75 

—  .17 

.00 

+  76.7 

54 

+  .10 

+  .01 

E 

+  70.2 

37 

-  .16 

+  .04 

e,  ' 

+  66.2 

49 

+  .07 

+  .05 

+  60.9 

150 

+  .11 

+  .08 

+  56.7 

116 

+  .21 

+  .07 

+  50.6 

122 

—  .15 

+  .01 

+  45.3 

94 

—  .01 

—  .04 

+  39.9 

107 

—  .11 

—  .02 

+  32.8 

25 

+  .27 

+  .08 

+  27.5 

111 

+  .28 

+  .14 

+  21.3 

118 

+  .14 

+  .14 

+  14.5 

120 

+  -12 

+  .09 

+  8.9 

162 

—  .04 

+  .05 

+  4.0 

83 

+  .28 

+  .06 

-  1.5 

83 

+  .14 

+  .09 

—  8.6 

87 

+  .19 

+  .14 

—  14.0 

47 

+  .18 

+  .17 

-  18.7 

35 

+  .08 

+  .21 

—  22.4 

31 

+  .24 

+  .24 

—  28.1 

39 

+  .28 

+  .28 

34.  i 

10 

+1.98 

T*- 

From  the  equator  to  the  pole  it  is  a  matter  of  indifference  whether  any  correction 

D  at  Greenwich  was  neglected  as  insensible 


be  applied  or  not.    The  correction 

during  this  period. 

With  m  =  5,  we  have:  — 


=  ±  ".65. 


524 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 

Residuals  in  order  of  riglit  ascension. 


[118J 


Declination  limits. 

Declination  limits. 

—  :y>°  to  +  90° 

—  30°  to  +  90° 

Mean  a 

ir> 

ro' 

Mean  a 

TT' 

V 

h. 

// 

Ji, 

// 

I 

179 

+  .06 

13 

130 

+  .03 

3 

87 

+  .01 

15 

185 

+  .12 

5 

146 

+  .05 

17 

152 

—  .03 

7 

101 

+  .02 

19 

200 

—  .10 

9 

116 

+  .12 

21 

181 

—  .12 

11 

164 

+  .12 

23 

120 

—  .13 

A  slight  correction  following  the  right  ascension  is  indicated.    It  differs,  however, 
quite  sensibly  from  that  shown  in  Gh  39,  and  I  have,  therefore,  undertaken  no  discussion. 

Pa  45. 

In  forming  *',  one  observation  is  given  weight  1;   two  to  five,  weight  2;  six  or 
more,  weight  3. 

Residuals  in  order  of  declination. 


Mean  S 

*•' 

>'o 

Form. 

Co 

0 

// 

n 

II 

+  86.6 

13 

—  .02 

+  .03 

.00 

+  76.0 

12 

+  .04 

+  .07 

.00 

-f  70.9 

21 

.00 

+  .10 

+  .05 

+  66.0 

12 

+  .18 

+  .13 

+  .11 

+  60.7 

41 

+  .18 

+  .16 

+  .17 

+  56.8 

29 

+  .21 

+  .19 

+  .21 

+  50.8 

39 

+  .27 

+  .23 

+  .25 

+  45.6 

31 

+  .24 

+  .26 

+  .89 

-f  39.9 

44 

+  .36 

+  .29 

+  .33 

+  33.0 

21 

+  .40 

+  .32 

+  .36 

+  26.9 

28 

+  .29 

+  .36 

+  .38 

+  21.0 

35 

+  .34 

+  .39 

+  .39 

+  14.5 
+    9.1 

38 
46 

+  .45 
+  .42 

+  .41 
+  .43 

+  .42 
+  .44 

+    4.3 

19 

+  .59 

+  .46 

+  .47 

—    1.9 

22 

+  .60 

+  .47 

+  .51 

—    8.4 

17 

+  .54 

+  .49 

+  .57 

—  14.1 

10 

+  .59 

+  .50 

+  .66 

—  19.4 

3 

+  .38 

4-    82 

—  23.  9 

3 

n   •  •w* 

[+1.04] 

I        •  **"• 

[+1.0  ] 

—  26.1 

3 

[+1.7  ] 

[+1.3  1 

L     I-*-*  "     J 

Column  "Form"  is  derived  from  the  expression  (Section  VI.) 

+  ".34  (sin  #+.503) 

Had  the  constant  +  ".34  been  increased  to  +  ".37,  the  accord  with  C0  would  have 
been  almost  perfect  down  to  —  8°.4.  The  curve  from  which  C0  is  taken  was  drawn 
without  the  slightest  reference  to  the  previous  correction. 


[119J 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          525 


The  value  of  JH,  taken  from  the  outstanding  residuals,  is  of  no  interest,  since,  on 
account  of  the  great  weight  given  to  Pa  45  in  the  discussion  of  standard  places,  it 
would  be  entirely  too  small.  In  the  introduction  to  the  fourth  volume  of  Poulkova 
observations,  we  have  a  thoroughly  reliable  discussion  of  the  probable  error  of  the 
declinations.  The  final  weights  were  founded  on  these  probable  errors,  which  increase 
rapidly  with  the  zenith  distance. 

From  the  final  residuals  (rf)  of  37  fundamental  and  circumpolar  stars  (excluding 
a  and  S  Ursae  Minoris),  I  derive  ±  ".273  as  the  probable  error  of  the  unit  of  adopted 
weights.  Supposing  the  average  weight  of  a  Poulkova  declination  4,  and  of  the  final 
J  3  for  1845,  80,  we  should  have  approximately  ±  ".29  as  the  probable  error  of  the  unit 
corresponding  to  a  probable  error  of  i  ".30,  as  given  in  the  introduction  of  volume  iv. 
A  like  discussion  of  the  residuals  (rt)  of  59  other  stars,  for  which  the  weight  of  a  posi- 
tion for  1845  is  40,  or  greater  (averaging  about  50),  gives  ±  ".285,  or  about  ±  ".305  for 
the  corrected  probable  error,  which  should  correspond  to  the  ±  ".30  assumed.  It  may 
therefore  be  assumed  that  the  weights  for  Pa  45,  constructed  in  the  manner  explained 
above,  are  entirely  reliable,  and  correspond  well  with  the  general  system  adopted  in 
the  definitive  discussion  of  A  8  and  A  //. 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

—  20°  to  +  90° 

—  20°  to  -f  90° 

Mean  a 

TT' 

'•„' 

Mean  a 

Tf' 

ro' 

h. 

II 

h. 

// 

1 

56 

+  .11 

13 

30 

+  .03 

•A 

20 

—  .11 

15 

51 

—  .04 

5 

37 

+  .01 

17 

50 

.00 

7 

33 

—  .06 

19 

50 

+  .10 

9 

33 

—  .06 

21 

45 

-  .09 

11 

47 

—  .02 

23 

31 

+  .05 

526         UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[120] 


Re  45. 

Residuals  in  order  of  declination. 


Mean  <5 

TT' 

ro 

Co 

o 

II 

II 

+  86.6 

[27] 

[+  -18] 

[+  -17] 

+  76.3 

22 

-j-  .53 

+  .62 

-(-  70.8 

28 

+  .72 

+  .61 

e       o 

+  66.4 

21 

+  .23 

+  -47 

—  =  £ 
f/ 

+  60.8 

45 

+  .05 

+  .30 

+  56.8 

36 

+  .30 

+  .16 

+  50.8 

45 

+  .02 

—  .04 

+  45.6 

38 

—  .06 

—  .18 

+  40.0 

42 

—  .47 

—  .34 

-f  33.4 

10 

—  .31 

—  .51 

-f-  27.4 

27 

—  .44 

—  .58 

+  21.1 

33 

—  .68 

—  .59 

+  14.3 

32 

—  .22 

—  .41 

+    8.8 

53 

—  .22 

—  .14 

+    3.9 

25 

—  .02 

+  .08 

—    1.4 

26 

+  .63 

+  .31 

—    8.6 

27 

+  .29 

+  .49 

—  14.0 

10 

+  .95 

+  .48 

-  19.0 

3 

+  .18 

+  .36 

—  22.  3 

9 

+  .36 

+  .25 

—  28.1 

13 

—  .31 

+  .06 

There  is  some  doubt  about  the  correction  from  +  75°  to  +  90°.     For  stars  observed 
both  above  and  below  the  pole,  it  is  probably  quite  small. 
With  m  =  5,  we  have: — 

E  =  ±  ".73 

I  adopt  ±  ".77,  the  mean  between  this  determination  and  that  for  Re  58. 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +  6° 

+  40°  to  —  30° 

+  40°  to  +  90° 

—  300  to  _)_  MO 

Mean  a 

7r' 

ro' 

71-' 

ro' 

TT' 

'o' 

x> 

'o' 

h. 

It 

// 

// 

;/ 

1 

3 

+  .10 

29 

+  .31 

37 

+  .05 

66 

+  .16 

3 

7 

—  .44 

17 

—  .03 

8 

+  .22 

25 

+  .06 

5 

9 

—  .10 

26 

+  .H 

20 

—  .12 

46 

+  .01 

7 

6 

—  .47 

26 

+  .06 

5 

—  .17 

31 

+  .03 

9 

4 

—1.70 

30 

—  .42 

16 

—  .34 

46 

—  .39 

'    11 

10 

+  .16 

22 

—  .05 

30 

—  .22 

52 

—  .15 

13 

13 

+  .33 

17 

+  .45 

21 

+  .40 

38 

+  .42 

15 

9 

+  .66 

26 

—  .06 

24 

—  .33 

50 

—  .19 

17 

6 

+  .03 

16 

+  .09 

34 

—  .11 

50 

—  .05 

19 

7 

—  .53 

26 

+  .11 

26 

+  .20 

52 

+  .15 

21 

12 

+  .60 

22 

+  .07 

32 

+  -14 

54 

+  .H 

23 

14 

—  .21 

28 

-  .19 

19 

—  .04 

47 

—  .13 

The  previous  discussion  (Section  VI.)  is  substantially  confirmed. 


[121J 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


527 


Wn  47. 
The  weights  are  adopted  as  they  result  from  the  combination  of  separate  years  in 

the  manner  explained  in  Section  V.    This  supposes  -  =  3. 

ei 

Residuals  in  order  of  declination. 


Mean  6 

TT' 

l'o 

cu 

o 

// 

// 

+  86.9 

72 

+  .10 

+  .13 

+  76.6 

51 

+  .46 

+  .14 

+  69.9 

19 

+  .24 

+  .10 

+  62.3 

35 

+  .07 

+  .02 

+  50.3 

31 

—  .14 

—  .05 

+  50.6 

73 

—  .16 

—  .05 

+  45.1 

31 

—  .23 

—  .05 

+  38.5 

58 

—  .05 

—  .05 

+  33.2 

20 

+  .66 

—  .06 

+  27.8 

89 

—  .01 

—  .11 

+  21.6 

83 

—  .24 

—  .19 

+  14.2 

122 

—  .35 

—  .28 

+  8.6 

111 

—  .35 

—  .34 

+  3.9 

74 

—  .37 

—  .35 

—  1.6 

49 

—  .51 

—  .33 

—  8.5 

63 

—  .16 

—  .28 

—  14.1 

54 

—  .30 

—  .24 

—  19.1 

22 

+  .06 

—  .19 

-  -22.3 

36 

—  .35 

—  .15 

—  28.5 

49 

—  .05 

—  .05 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +  5° 

+  40°  to  —  30° 

+  40°  to  +  90° 

—  30°  to  +  90° 

Mean  .< 

TT' 

I'D' 

,_/ 

'V 

fi" 

I'O 

T' 

>o' 

h. 

// 

// 

it 

// 

1 

10 

+  .02 

56 

+  .19 

43 

—  .10 

99 

+  .06 

3 

49 

+  .01 

56 

—  .08 

18 

—  .70 

74 

—  .23 

5 

24 

—  .33 

70 

—  .56 

12 

—  .40 

82 

—  .53 

7 

25 

—  .13 

58 

—  .20 

10 

+  .10 

68 

—  .16 

9 

10 

—  .50 

46 

—  .20 

11 

+  .21    . 

57 

—  .12 

11 

11 

—  .60 

37 

—  .34 

29 

+  .02 

66 

—  .18 

13 

18 

—  .02 

37 

—  .10 

14 

+  .50 

51 

+  .06 

15 

43 

+  .34 

102 

+  .30 

28 

+  .65 

130 

+  .37 

17 

31 

+  .15 

58 

+  .25 

:« 

+  .16 

93 

+  .21 

19 

30 

+  .15 

149 

+  .25 

1.3 

.00 

102 

+  .20 

21 

44 

—  .01 

95 

+  .06 

66 

—  .04 

161 

+  .02 

23 

27 

—  .04 

60 

—  .08 

23 

—  .10 

83 

—  .08 

From  discussion  of  the  values  of  r0'  in  the  final  grouping  (— 30°  to  +90°),  I 
derive: — 

—  ".27  sin  a  —  ".08  cos  a. 

Examination  of  Wn  56  and  Wn  64  shows  that  they  are  in  need  of  a  similar  cor- 
rection ;  and  the  separation  into  zones  renders  it  highly  probable  that  this  correction 
is  almost  equally  applicable  to  all  limits  of  declination. 


528  UNITED  STATES  .NORTHERN  BOUNDARY  COMMISSION. 

For  Wn  56,  we  have : — 


[122 


and  for  Wn  64, 


—  ".16  sin  a  —  ".19  cos  a; 

—  ".22  sin  a  —  ".12  cos  a. 


The  same  form  of  correction  is  indicated  in  Wn  70. 

It  is  undoubtedly  real  and  sensibly  constant  for  the  Washington  mural  circle 
throughout  the  period  of  its  use.  From  the  combined  residuals  (—  30°  to  +  90°)  of 
Wn  47,  56,  and  64,  we  have: — 

-  (".21  ±  ".03)  sin  a  -  (".12  ±  ".03)  cos  a 

as  the  correction ;  and  it  is  adopted. 

It  reduces  the  sums  of  squares  as  follows : — 


Year. 

Before. 

After. 

1847 

144 

101 

1856 

258 

236 

1864 

179 

165 

From  the  final  residuals  for  1847,  with  m  =  7,  we  have: — 

£  =  ±".74. 

Ce48. 

The  weights  are  derived  in  the  manner  explained  under  Ce  40. 
Residuals  in  order  of  declination. 


Mean  <5 

IT' 

ra 

Co 

o 

a 

it 

+  87.9 

35 

+  .28 

.00 

+  76.9 

15 

—  .15 

.00 

+  70.2 

19 

—  .01 

.00 

+  65.6 

20 

+  .03 

—  .09 

+  61.0 

62 

—  .21 

—  .23 

+  56.6 

36 

—  .44 

—  .37 

+  49.5 

49 

—  .51 

—  .58 

+  45.4 

64 

—  .58 

—  .6H 

+  39.0 

35 

—1.19 

—  .82 

+  32.6 

16 

—  .71 

—  .86 

+  27.8 

58 

—  .78 

—  .75 

+  21.3 

60 

—  .42 

—  .41 

+  14.5 

82 

—  .02 

—  .09 

+    9.1 

68 

—  .02 

—  .05 

+    4.2 

29 

—  .22 

—  .05 

—    1.0 

27 

—  .02 

—  .08 

—    8.6 

38 

—  .15 

—  .12 

—  14.1 

15 

+  .13 

—  .12 

—  18.5 

9 

+  .20 

—  .09 

—  21.  5 

6 

—  .9 

—  .09 

—  26.2 

3 

—  .8 

—  .03 

With  m  =  5,  we  have: — 

E  =  ±  ".62 

.60  is  adopted,  as  explained  under  Ce  40. 


[123J 


RKPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  11. 

Residuals  in  order  of  rigJit  ascension. 


529 


Declination  limits. 

Decl'nation  limits. 

—  30°  to  +90° 

—  30C  to  +90° 

Mean  a 

4 

TO' 

Mean  a 

71-' 

>V 

h. 

II 

A. 

// 

1 

84 

+  .07 

13 

52 

+  .10 

3 

29 

—  .19 

15 

50 

—  .08 

5 

74 

+  .06 

17 

47 

—  .09 

7 

47 

—  .03 

19 

119 

—  .09 

9 

53 

—  .04 

21 

79 

—  .02 

11 

73 

+  .01 

23 

35 

+  .21 

Gh  61. 

Residuals  in  order  of  declination. 


Mean  t 

TT' 

r<> 

Co 

o 

// 

II 

+  86.6 

77 

—  .16 

—  .13 

e 

+  76.4 

55 

—  .07 

—  .14 

7,  =  4 

+  70.6 

56 

—  .25 

—  .15 

+  66.4 

23 

—  .22 

—  .16 

+  61.1 

95 

—  .14 

—  .17 

+  56.7 

78 

—  .17 

—  .19 

+  50.9 

102 

—  .15 

—  .21 

+  45.6 

62 

—  .26 

—  .20 

+  39.4 

98 

—  .17 

—  .15 

+  32.5 

82 

+  .05 

—  .03 

+  27.3 

147 

—  .04 

+  .06 

+  21.2 

147 

+  .15 

+  .16 

+  14.5 

165 

+  .28 

+  .18 

+  9.0 

218 

+  .23 

+  .15 

+  4.1 

102 

.00 

+  .1U 

—  1.7 

129 

—  .01 

+  .03 

—  8.5 

110 

—  .07 

.00 

—  14.  1 

52 

+  .01 

+  .03 

—  18.8 

36 

+  .17 

+  -11 

—  22.4 

48 

+  .31 

+  .16 

—  28.2 

43 

—  .03 

+  .22 

With  m  =  5,  we  have: — 


E  = 


.70. 


There  is  «i  trace  of  the  same  peculiarity  in  the  values  of  r0-,  as  has  appeared  with 
Gh  45.  In  any  case,  the  required  correction  is  so  small  that  its  ueglect  is  of  little 
consequence  to  the  final  result. 


530          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

—  30°  to  +5° 

—  30°  to  +90° 

Mean  a 

rr' 

n,' 

TT' 

r,' 

i 

27 

II 

—  .04 

214 

—  .15 

3 

38 

—  .14 

94 

+  .04 

5 

47 

+  .01 

157 

+  .06 

7 

25 

—  .15 

131 

—  .11 

9 

14 

—  .20 

129 

-1-  .01 

11 

39 

+  .06 

177 

+  -14 

13 

60 

+  .10 

126 

+  .13 

15 

54 

+  .01 

195 

+  .03 

17 

27 

—  .20 

169 

—  .06 

19 

52 

+  .05 

183 

+  .03 

21 

40 

—  .31 

174 

—  .02 

23 

54 

—  .06 

139 

—  .01 

So  51. 
Residuals  in  order  of  declination. 


Mean  <5 

TT' 

ra 

Co 

o 

n 

II 

+  45.8 

4 

+  1.06 

+  38.6 

13 

—    .03 

+    .44 

«         0 

+  33.2 

4 

—    .04 

+    .58 

—  =» 

£, 

+  27.5 

33 

+    .77 

+    -74 

/ 

+  21.3 

40 

+    .88 

+     .87 

+  14.5 

46 

+    .92 

+     .99 

+    8.7 

42 

+  1.23 

+    .05 

+     3.7 

26 

+  1.01 

+     .09 

—    2.2 

14 

+  1.09 

+    .12 

—    8.5 

28 

+  1.22 

+    .12 

—  14.1 

15 

+  1.16 

+    .10 

—  18.9 

12 

+    .81 

+    .06 

—  22.5 

16 

+    .95 

+     .08 

—  28.2 

17 

+    .90 

+  1.00 

—  34.2 

1 

+    .25 

+    .96 

—  41.9 

2 

+  1.24 

+     .91 

—  52.6 

1 

+    .94 

+    .79 

—  59.  6 

6 

+     .82 

+    .62 

—  75.1 

3 

+    .28 

+    .28 

REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 

Residuals  in  order  of  right  ascension. 


531 


Declination  limits. 

Declination  limits. 

—  30°  to  +  40° 

—  30°  to  +  40° 

Mean  a 

»* 

ro' 

Mean  a 

K> 

ro' 

h. 

// 

h. 

// 

0.9 

24 

—  .37 

13.1 

81 

—  .16 

3.1 

22 

+  .15 

14.9 

30 

—  .07 

5.1 

29 

+  .49 

16.7 

19 

—  .31 

7.1 

32 

+  .07 

19.0 

40 

—  .16 

9.3 

27 

+  .10 

21.2 

22 

-  .19 

11.3 

22 

+  .53 

22.9 

18 

—  .66 

There  is  an  evident  progression  of  rc'  with  a.    The  discussion  gives,  as  the  correc- 
tion to  be  applied : — 

+  (".24  ±  ".07)  sin  a  —  (".185  ±  ".075)  cos  a. 

There  is  some  reason  to  expect  such  a  correction  for  this  series,  and  it  is  adopted. 
With  m  =  6,  we  have: — 

±  ".86. 

Ps  53. 

Residuals  in  order  of  declination. 


Mean  c! 

•K1 

ro 

C0 

•' 

o 

II 

// 

+  86.3 

37 

—  .10 

+  .06 

e       „ 

+  76.7 

23 

+  .18 

+  .19 

o 

e. 

+  70.6 

31 

+  .38 

+  .25 

i 

+  66.0 

18 

+  .20 

+  .28 

+  61.9 

29 

-j-  .40 

+  .29 

+  56.5 

40 

+  .29 

+  .28 

+  50.6 

33 

+  .05 

+  .23 

+  46.0 

16 

+  .48 

+  .19 

+  39.5 

26 

+  .17 

+  .12 

+  33.2 

13 

—  .03 

+  .05 

+  27.7 

30 

—  .08 

-  .03 

+  21.5 

38 

—  .15 

—  .10 

+  14.4 

38 

—  .01 

—  .19 

+    8.7 

49 

—  .31 

—  .28 

-t-3.9 

33 

—  .44 

—  .34 

—    1.2 

28 

—  .15 

—  .37 

—    9.0 

19 

—  .47 

—  .31 

—  14.1 

19 

—  .16 

—  .21 

—  18.7 

13 

—  .21 

—  .06 

—  22.3 

10 

+  .12 

+  .12 

—  28.6 

13 

+  .92 

+  .6 

With  m  =  5,  we  have: — 


E=±  ".57. 


532 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 

Residuals  in  order  of  right  ascension. 


[126] 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +  5° 

+  40°  to  —  30° 

—  30°  to  +  90° 

Mean  a 

7T1 

ro' 

K1 

ro' 

TT' 

ro 

h. 

II 

// 

II 

1 

9 

—  .08 

39 

—  .02 

59 

—  .05 

3 

16 

+  .35 

24 

+  .10 

41 

+  .18 

5 

17 

—  .02 

31 

+  .26 

42 

+  .02 

7 

6 

+  .20 

25 

+  -17 

31 

+  .15 

9 

3 

+  .60 

18 

—  .09 

27 

—  .02 

11 

8 

—  .45 

22 

—  .26 

56 

—  .11 

13 

13 

+  .13 

20 

+  .10 

44 

—  .11 

15 

16 

—  .22 

27 

—  .14 

55 

—  .11 

17 

8 

+  .05 

20 

—  .44 

50 

—  .18 

19 

9 

.00 

36 

—  .21 

48 

+  .12 

21 

10 

—  .10 

35 

+  .01 

61 

+  .15 

23 

15 

+  .10 

5 

+  .60 

24 

+  .35 

So  55. 
Residuals  in  order  of  declination. 


Mean  d 

if 

'o 

Co 

o 

/* 

it 

+  45.8 

1 

—  .56 

• 

+  38.3 

2 

+1.19 

+  .50 

-  =  2. 

e; 

+  24.  5 

4 

+  .67 

+  .48 

+  20.9 

13 

+  .51 

+  .45 

+  14.2 

27 

+  .30 

+  .29 

+    8.3 

29 

—  .03 

+  .18 

+    3.8 

15 

+  .46 

+  .18 

—    1.9 

12 

+  .45 

+  .32 

—    8.7 

20 

+  .35 

+  .39 

—  14.0 

12 

+  .55 

+  -17 

—  19.0 

7 

—  .07 

—  .03 

—  2-2.2 

11 

—  .58 

—  .10 

—  28.6 

12 

—  .31 

—  .05 

—  42.8 

+    34 

4-    27 

—  51.8 

1 

1        •  "^ 

+  .42 

-f-      .    Aft 

+  .24 

—  59.3 

3 

+  .19 

+  .12 

—  78.3 

2 

—  .49 

.00 

With  m  =  6,  we  have: — 


=  ±  ".91. 


[127] 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 

Residuals  in  order  of  right  ascension. 


533 


Declination  limits. 

Declination  limits. 

—  30°  to  +  40° 

—  30°  to  -f  40° 

Mean  & 

v1 

>•„' 

Mean  6 

TT' 

»•„' 

h. 

// 

h. 

// 

1.1 

7 

+  .04 

12.9 

19 

—  .41 

2.5 

13 

—  .17 

15.2 

10 

+  .01 

5.0 

14 

—  .09 

1C.  7 

16 

—  .15 

7.0 

8 

—  .38 

19.2 

25 

+  .02 

9.4 

13 

—  .39 

21.2 

13 

4-  .40 

11.3 

19 

—  .10 

22.7 

8 

+  .21 

If  there  is  a  real  variation  of  the  correction,  proceeding  with  the  right  ascension, 
it  is  apparently  of  an  entirely  different  nature  from  that  adopted  for  So  51.  The 
weights  are  small,  and  the  observations  are  assumed  to  be  practically  Jree  from  any 
error  of  this  kind. 

Wn56. 

Residuals  in  order  of  declination. 


Mean  6 

«•' 

'o 

Co 

• 
o 

// 

II 

+  86.1 

63 

—  .18 

—  .07 

+  76.7 

20 

—  .05 

+  .10 

-  —  4 

et 

+  70.2 

6 

+  .55 

+  -I? 

H-  66.3 

4 

4  .30 

+  .18 

+  62.  1 

27 

+  .50 

+  -17 

+  50.  1 

15 

+  .24 

+  -14 

+  50.3 

51 

—  .16 

4  .10 

+  45.3 

30 

—  .10 

+  .05 

4  38.9 

64 

+  .08 

-  .01 

+  32.0 

15 

+  .37 

—  .06 

+  27.6 

80 

—  .05 

—  .11 

+  21.5 

79 

—  .23 

—  .17 

4  14.5 

75 

—  .16 

—  .24 

+  8.7 

86 

—  .16 

—  .26 

4  4.2 

62 

—  .69 

—  .27 

—  1.5 

57 

—  .26 

—  .25 

—  8.5 

58 

—  .13 

—  .19 

—  14.0 

34 

—  .08 

—  .11 

—  18.9 

20 

—  .28 

—  .04 

—  22.2 

20 

4  .09 

4  .02 

—  .  28.  5 

31 

H-  .19 

4  .13 

The  probable  error,  E,  is  derived  from  the  outstanding  residuals  corrected  further 
for  the  effect  of  terms  in  a  given  under  Wn  47. 
With  m  =  6,  we  have: — 

E=±  ".88. 

With  a  smaller  value  of  -,  we  should  have  a  smaller  and  probably  more  accurate 

•/ 
value  of  E. 


534          UNITED  STATES  NOETHEEN  BOUNDAKY  COMMISSION.         [128] 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +  5° 

+  40°  to  —  30° 

4.  40°  to  +  90° 

—  30°  to  +  90° 

Mean  a 

IT1 

»o' 

7T7 

ro; 

ic1 

I'o' 

9? 

ro' 

ft. 

// 

// 

II 

// 

1 

19 

—  .  35 

61 

—  .07 

22 

—  .10 

83 

—  .08 

3 

27 

—  .77 

42 

—  .75 

10 

—1.00 

52 

—  .80 

5 

18 

—  .64 

48 

—  .41 

12 

—  .45 

60 

—  .41 

7 

12 

—  .22 

49 

—  .01 

14 

—  .10 

63 

—  .04 

9 

3 

—  .30 

24 

+  .25 

10 

+  .13 

34 

+  .21 

11 

16 

+  .19 

40 

+  -17 

25 

+  .46 

65 

+  .28 

13 

30 

—  .02 

47 

.00 

12 

+  .08 

59 

+  .02 

15 

26 

+  .48 

72 

+  .34 

21 

—  .23 

93 

-f  .21 

17 

17 

+  .27 

53 

+  .28 

28 

+  .05 

81 

+  .ao 

19 

18 

—  .25 

81 

—  .04 

21 

—  .19 

102 

—  .07 

21 

33 

+  .22 

76 

+  .07 

38 

—  .05 

114 

+  .03 

23 

43 

+  .18 

70 

+  .12 

11 

—  .06 

81 

+  -11 

For  further  explanation  see  Wu  47. 

Ps  56. 
Residuals  in  order  of  declination. 


Mean  6 

vr7 

ra 

Co 

o 

ft 

*/ 

+  86.6 

26 

—  .35 

—  .32 

1  =  2 

Ei 

+  76.6 

15 

—  .31 

—  .22 

/ 

+  70.8 

15 

—  .04 

—  .16 

+  66.2 

10 

+  .06 

—  .13 

+  61.0 

30 

—  .22 

—  .10 

+  56.7 

32 

—  .17 

—  .09 

+  50.4 

25 

+  .05 

—  .11 

+  45.2 

30 

—  .  05 

—  .15 

+  39.4 

25 

—  .47 

—  .21 

+  33.0 

26 

-  .52 

—  .26 

+  27.6 

37 

—  .17 

—  .30 

+  21.1 

48 

—  .26 

—  .35 

+  14.5 

53 

—  .37 

—  .36 

+  8.9 

70 

—  .38 

—  .36 

+  4.0 

32 

—  .32 

—  .35 

—  1.7 

47 

—  .31 

—  .33 

—  8.5 

43 

—  .29 

—  .23 

—  14.1 

15 

—  .07 

—  .08 

—  18.8 

12 

+  .11 

+  .12 

—  21.9 

13 

+  .20 

+  .12 

—  28.1 

17 

+  .42 

+  .50 

After  the  further  correction  depending  on  a  (to  be  explained),  the  outstanding 
residuals,  with  m  =  7,  give: — 

E=  i  ".46. 


[129]  REPORT  OF  TEE  CHIEF  ASTRONOMER,  APPENDIX  H.          535 

Residuals  in  order  of  rifjht  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +  6° 

+  40°  to  —  30° 

.(.  4QO  to  _j_  900 

—  30°  to  +  90° 

Mean  « 

*• 

r0' 

TT' 

fg 

TT' 

n/ 

TT' 

r»' 

ft. 

n 

,1 

// 

II 

1 

8 

-  .15 

21 

+  .05 

25 

+  .23 

46 

+  .15 

3 

11 

+  .15 

23 

+  .13 

13 

+  .01 

36 

+  .08 

5 

15 

+  .07 

37 

+  .09 

13 

H-  .12 

50 

+  .10 

7 

4 

+  .70 

32 

+  .17 

4 

-1-  .10 

36 

+  .16 

9 

4 

+  .30 

24 

•f  .25 

4 

+  .30 

28 

+  .25 

11 

10 

+  .55 

33 

+  .11 

27 

-j-  .09 

60 

+  .10 

13 

22 

+  .21 

30 

+  .15 

22 

—  .11 

52 

+  .04 

15 

19 

+  .04 

40 

—  .05 

23 

—  .01 

63 

—  .03 

17 

10 

-  .35 

33 

—  .25 

19 

—  .13 

52 

—  .21 

19 

20 

—  .28 

50 

—  .31 

14 

—  .01 

64 

—  .25 

21 

19 

+  .01 

44 

—  .17 

20 

—  .03 

64 

—  .13 

23 

25 

—  .30 

38 

—  .24 

11 

—  .23 

49 

—  .23 

Tbe  dependence  of  r0'  on  right  ascension  is  undoubted. 
From  the  column  —  30°  to  +  90°,  1  derive: — 

+  ".19  sin  a  —  ".07  cos  «. 
From  the  tables  exhibited  success!  vely  under  Ps  60,  Ps  64,  and  Ps  66,  I  find : 


Year. 

Formula  of 

correction. 

1860 
1864 
1866 

+  .  18  sin  a 
4-  .  17  sin  a 
+  .  19  sin  a 

—  .  04  cos  a 
—  .  00  cos  a 
—  .  10  cos  n 

From  the  proper  combination  of  the  four  sets,  we  have: — 

+  (".20  ±  ".Ot)  sin  a  —  (".05  ±  ".01)  cos  «. 

This  is  adopted  as  the  definitive  correction  for  each  of  the  four  catalogues,  since 
there  appears  to  be  no  marked  increase  with  the  time. 

This  correction  might  be  approximately  computed  in  the  following  manner: — 
If  in  the  definitive  formula  of  correction*  for  the  declinations  of  the  Fundamenta 
south  of  +  51°,5  we  substitute  30°  for  S,  we  shall  have  for  that  part  of  the  correction 
depending  on  «: — 

—  ".82  sin  a  +  ".07  cos  a. 

If,  further,  we  suppose  that  the  mean  declination  of  the  stars  of  the  Paris  standard 
catalogue,  chiefly  used  for  obtaining  zenith  points,  is  about  +31°,  that  the  catalogues 
making  up  the  Paris  standard  are  free  from  errors  depending  on  «,  and  that  their 
mean  epoch  is  about  1845,  we  shall  have  for  the  epoch  1SG1  (about  the  mean  of  the 
entire  Paris  series)  as  a  correction  to  Paris  observed  declinations : — 

(  +  ".82  sin  a  +  ".07  cos  a )  x  ™  =  +  ".146  sin  a  -  ".012  cos  «. 

Of  course,  if  the  mean  epoch  of  the  catalogues  making  up  the  standard  is  earlier 
than  1845,  this  correction  will  be  larger. 

•  SrcttMI.   VII. 


536          UNITED  STATES  NORTHERN  BOUND AEY  COMMISSION. 


[130J 


Bs  56. 
Residuals  in  order  of  declination. 


Mean  d 

IT 

»'o 

Co 

+  86.9 

27 

// 

+  .30 

// 

+  .24 

c  —1 

+  76.4 

19 

+  .23 

+  .31 

—  ___  O 

e, 

+  09.8 

11 

+  .03 

+  .31 

+  01.  8 

20 

+  .30 

+  .25 

-t-  56.9 

17 

+  .15 

+  .13 

+  50.6 

39 

-  .07 

—  .10 

+  45.6 

16 

—  .93 

—  .33 

+  38.3 

20 

—  .64 

—  .52 

+  32.8 

24 

—  .35 

—  .50 

+  27.4 

36 

—  .23 

—  .41 

+  21.2 

34 

—  .71 

—  .45 

+  14.2 

37 

—  .54 

—  .64 

+  8.5 

36 

—  .44 

—  .72 

+  4.6 

24 

—1.50 

—  .74 

—  2.0 

21 

—  .73 

—  .59 

—  8.4 

18 

+  .18 

—  .30 

—  14.1 

18 

—  .23 

—  .21 

—  19.3 

9 

—  .11 

—  .23 

—  22.2 

11 

—  .37 

—  .24 

—  28.7 

10. 

—  .73 

—  .29 

1 

With  m  =  7,  we  have: — 


E  =  ±  ".95 
Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

+  40°  to—  30° 

+  40"  to  _|_  goo 

—  30°  to  +90° 

Mean  a 

V? 

r»' 

•K1 

»o' 

It1 

rj 

h. 

II 

// 

n 

1 

21 

—  .no 

19 

—  .17 

40 

—  .36 

3 

13 

—1.76 

6 

—  .17 

19 

—1.25 

5 

14 

+  -41 

t 

+  .21 

21 

+  .35 

7 

10 

+  .92 

1 

+  .20 

11 

+  .85 

9 

25 

+  .14 

13 

+  .40 

38 

+  .26 

11 

22 

—  .16 

16 

+  .32 

38 

+  .04 

13 

10 

—  .01 

11 

+  .11 

21 

+  .05 

15 

46 

+  .28 

13 

-  .08 

59 

+  .21 

17 

30 

+  .03 

19 

+  .09 

49 

+  .05 

19 

43 

+  .06 

12 

—  .04 

55 

+  .04 

21 

25 

—  .29 

25 

—  .13 

50 

—  .21 

23 

34 

—  .05 

10 

—  .24 

44 

—  .09 

A  considerable  correction  depending  on  a  is  indicated.    The  residuals  from  limits 

—  30°  to  +  900  give  :— 

—  ".04  sin  a  —  ".28  cos  a. 

But,  since  this  result  is  entirely  opposed  to  that  derived  from  the  later  Brussels 
work,  the  correction  is  neglected.  This  could  do  but  little  harm,  since  the  observations 
receive  small  weight. 


[131]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 

Ce5G. 

weights  are  formed  as  in  the  two  preceding  Cambridge  catalogues. 
•     Residuals  in  order  of  declination. 


537 


Mriui  i 

TT' 

»o 

Co 

o 

// 

II 

+  87.5 

32 

—  .10 

—  .22 

+  75.8 

12 

—  .50 

—  .30 

+  70.7 

12 

—  .51 

—  .35 

+  65.7 

11 

-  .03 

—  .43 

+  00.7 

44 

—  .64 

—  .53 

+  56.9 

30 

—  .45 

—  .69 

+  49.2 

28 

—1.25 

—1.16 

+  45.4 

30 

—1.39 

—1.36 

-j-  39.3 

28 

—1.47 

—1.45 

+  32.7 

14 

—1.22 

—1.35 

+  27.9 

42 

—1.21 

—1.22 

+  20.5 

28 

—  .96 

—  .92 

+  14.5 

52 

—  .59 

—  .66 

+    8.9 

33 

—  .56 

—  .58 

+    5.2 

9 

—  .96 

—  .57 

—    0.9 

10 

—  .53 

—  .55 

—    8.3 

19 

—  .68 

—  .50 

—  13.9 

12 

—  .32 

—  .47 

—  19.1 

4 

—  .29 

—  .43 

—  21.6 

3 

+  .77 

—  .41 

—  26.2 

4 

—  .47 

—  .38 

With  m  =  5,  we  have: — 


E  =  ±  ".GO. 
Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

—  30°  to  +90° 

—  30°  to  +90° 

Mean  a 

7T7 

»'c' 

Mean  a 

•K1 

n>' 

h. 

// 

h. 

// 

1 

41 

+  .09 

13 

39 

+  .33 

3 

8 

+  .06 

15 

54 

—  .11 

5 

22 

+  .02 

17 

44 

—  .10 

7 

27 

+  .01 

19 

64 

+  .12 

9 

41 

—  .24 

21 

51 

-  .09 

11 

48 

—  .02 

23 

26 

+  .29 

538 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[13<JJ 


Gh  57. 

Residuals  in  order  of  declination. 


Mean  6 

•K1 

To 

Co 

c 

it 

if 

+  86.7 

45 

+  .04 

+  .02 

+  7G.2 

39 

+  .07 

-1-  .08 

-  —  3 

-j-  70.4 

42 

+  .19 

+  .15 

1 

+  GO.  7 

31 

+  .34 

+  .19 

-j-  61.2 

63 

+  .24 

+  .23 

+  5(i.7 

34 

+  .18 

+  .22 

+  51.  0 

66 

+  .26 

+  .16 

+  45.4 

36 

+  .10 

+  -11 

+  40.2 

63 

+  .05 

+  .11 

+  32.5 

54 

+  .26 

+  .20 

+  27.3 

94 

+  .25 

+  .29 

+  21.2 

110 

+  .34 

+  .36 

+  14.  C 

110 

+  .39 

+  .38 

+    9.0 

146 

+  .42 

+  .34 

+    4.1 

71 

+  .20 

+  .26 

—    1.5 

84 

—  .04 

+  -17 

—    8.6 

69 

+  .22 

+  .20 

—  14.1 

30 

+  .31 

+  .'*5 

—  18.8 

22 

+  .43 

+  .26 

—  22.3 

31 

+  .39 

+  .26 

—  2H.2 

29 

+  .02 

+  .22 

With  m  ==  6,  we  have: — 

E  =  ±  ".46. 

The  same  quantity  for  1864  is  ±  ".49;  ±  ".48  is  adopted  in  constructing  the  definitive 
system  of  weights.    Mr.  Stone  linds  (Month.  Not.,  29-324)  for  zenithal  value  of «  i  ".47, 

and  this  becomes  ±  ".85  at  70°.    It  is  probable,  therefore,  that  -  is  taken  too  small. 

£/ 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +5° 

—  30°  to  +  40° 

—  30°  to  +90° 

Mean  a 

TT' 

TO' 

V 

n,' 

*•' 

n,' 

ft. 

ft 

it 

// 

1 

1C 

—  .25 

80 

+  .01 

129 

—  .03 

3 

20 

+  .08 

45 

+  .07 

55 

+  .05 

5 

24 

+  .01 

78 

+  .07 

109 

+  .08 

7 

14 

+  .15 

82 

+  .15 

91 

+  .15 

9 

8 

+  .20 

60 

+  .06 

85 

+  .08 

11 

30 

—  .12 

73 

—  .05 

99 

.00 

13 

39 

—  .25 

56 

—  .25 

78 

—  .16 

15 

39 

+  .11 

83 

—  .01 

103 

—  .02 

17 

16 

—  .45 

66 

—  .02 

127 

+  .02 

19 

24 

+  .07 

90 

—  .05 

134 

—  .05 

21 

27 

—  .04 

77 

—  .05 

14fi 

—  .03 

23 

38 

—  .00 

71 

+  .05 

93 

+  .10 

[J33]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          539 


C.  G.  H.  58. 
Residuals  in  order  of  declination. 


Mean  i! 

TT' 

»-o 

Co 

o 

// 

II 

+  49.8 

3 

—  3.47 

F 

|—        ~*Vt   W 

+  44.7 

3 

—  1.27 

_  0 

e    —  ft 

n   ™  * 

+  38.6 
-f  32.9 
+  27.2 
+  21.2 
+  14.5 
+    8.9 
+    3.9 

8 
10 
35 
48 
45 
58 
31 

.00 
—    .23 
+     .10 
—    .21 
—    .13 
—    .20 
—    .19 

—  .66 
—  .10 
—  .05 
—  .09 
—  .15 
—  .18 
—  .21 

1 
The  weights  of  the  last 
five  groups  are  arbi- 
trarily selected,  and 
have  no  reference  to 
the      scale    adopted 
above. 

—    0.8 

31 

—    .23 

—  .23 

—    8.5 

38 

—    .26 

—  .26 

—  14.1 

19 

—    .38 

—  .21 

—  18.9 

12 

+     .21 

—  .16 

—  22.  4 

19 

+     .17 

—  .13 

—  28.  0 

20 

—     .08 

—  .07 

—  34.9 

2 

—    .01 

.00 

—  42.1 

4 

+     .18 

+  .09 

—  52.1 

2 

-    .30 

+  -17 

—  58.7 

6 

+     .43 

+  .25 

—  75.1 

3 

+     .36 

+  .19 

With  MI  =  4,  we  have : — 


E  =  ±  ".50. 


Dr.  Gylden  finds  (V.  J.  8.,  X,  197)  for  e  from  15°.2  to  41°.4  zenith  distance  ±  ".45,  and 

"24* 
but  a  slight  increase  to  60°  Z.  D.    Assuming  E,  to  be  db  -^=-  =  ±  ".17,  \ve  have:— 

E  =  ±  ".48, 

for  the  zenith.    The  above  value,  ±  ".50,  appears  to  be  quite  trustworthy. 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +5°       ;, 

+  5C  to  +  40° 

—  30°  to  +40° 

Moan  a 

v' 

iV 

if 

ra' 

JT' 

ro 

h. 

// 

It 

II 

1 

10 

+  .15 

27 

+  -14 

37 

+  -14 

3 

12 

+  .03 

9 

-  .16 

21 

—  .05 

5 

18 

+  .10 

22 

—  .19 

40 

—  .07 

7 

10 

+  .20 

30 

+  .13 

40 

+  .15 

9 

5 

+  .10 

21 

—  .01 

26 

+  -01 

11 

17 

+  .21 

19 

—  .07 

36 

—  .12 

13 

19 

.00 

3 

—  .17 

22 

—  .02 

15 

19 

+  .37 

14 

—  .08 

33 

+  .14 

17 

9 

+  .04 

15 

—  .10 

24 

—  .05 

19 

14 

+  .20 

25 

+  .04 

39 

+  .10 

21 

14 

—  .22 

12 

+  .52 

26 

+  .12 

23 

21 

—  .08 

10 

—  .03 

31 

—  .07 

'  Pr.  Oylden  finds  ^  ".24  :>s  the  probable  minimum  error  of  a  difterence  of 
declination,  Gh  57— C.  G.  H.  r.8  (V.  J.  S..  X.  200). 


540  UNITED  STATES  NORTHERN    BOUNDARY  COMMISSION.          [134] 


Re  58. 

Residuals  in  order  of  declination. 


Mean  <5 

JT* 

»o 

Co 

0 

// 

If 

+  86.3 
+  75.8 

17 
14 

[-  -02] 
[+  .11] 

+  .40 
+  .  6sJ 

1=2 

E, 

+  71.3 

12 

-j-  .82 

+  -71 

I 

+  GO.  9 

11 

+  .76 

+  .71 

+  61.  I 

24 

+  .55 

+  .62 

+  56.7 

26 

+  .52 

+  .51 

+  50.6 

27 

+  .35 

+  .23 

+  45.8 

15 

+  .48 

—  .07 

+  39.4 

30 

—  .67 

—  .45 

+  33.1 

24 

—  .63 

—  .71 

+  27.4 

30 

—  .82 

—  .77 

+  21.1 

34 

—  .63 

—  .CO 

+  14.6 

35 

—  .41 

—  .32 

+    9.1 

48 

—  .11 

—  .03 

+     4.3 

23 

+  .18 

+  .24 

—     1.5 

29 

+  .59 

+  .57 

—    8.5 

22 

+  .92 

+  .76 

—  15.9 

17 

+  .6 

+  .7? 

—  22.4 

11 

+1.1 

+  .54 

—  27.9 

12 

—  .6 

+  .22 

With  m  =  5,  we  have : — 

E  =  ±  ".80. 
±  ".77  is  adopted.     (See  Re  45.) 

Iii  drawing  the  curve  I  have  been  much  assisted  by  the  very  complete  dis- 
cussion of  this  catalogue  in  Volume  V.  of  the  Vicrteljahrsschrift  der  Ast.  Ges.  The 
examination  for  terms  in  a,  however,  fails  to  confirm  Table  IV.,  given  in  the  place  cited, 
as  will  appear  from  the  following  : 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +  5° 

—  30°  to  +  40° 

—  30°  to  +90° 

Mean  a 

TT' 

ro' 

7T' 

ro'. 

IT' 

r<> 

ft. 

if 

// 

a 

1 

4 

—1.45 

28 

—  .35 

54 

—  .01 

3 

7 

—  .37 

13 

—  .30 

19 

+  .02 

5 

12 

—  .32 

28 

—  .51 

37 

—  .32 

7 

6 

—  .15 

31 

+  .05 

34 

—  .01 

9 

3 

+  .90 

25 

—  .01 

37 

—  .12 

11 

9 

+  .23 

25 

—  .02 

37 

—  .25 

13 

11 

+  .01 

19 

+  .25 

32 

-f  .26 

15 

13 

—  .06 

29 

+  .17 

45 

—  .18 

17 

5 

—  .06 

25 

—  .35 

44 

—  .32 

19 

9 

—  .31 

31 

—  .07 

44 

+  .04 

21 

9 

+  .83 

27 

+  .53 

41 

+  .51 

23 

14 

—  .03 

26 

+  .27 

43 

+  .36 

The  correction  depending  on  a,  if  it  exists,  is  so  uncertain,  from  the  small  weight, 
that  no  attempt  at  discussion  is  made.  The  probable  error  of  the  residuals  in  last 
column  varies  from  ±  ".12  to  ±  ".18. 


[135]  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          541 

Ps  60. 
Residuals  in  order  of  declination. 


Mean  3 

71-' 

'"0 

Co 

o 

a 

// 

+  86.8 

20 

—  .15 

—  .19 

1_0 

+  70.  (i 

13 

—  .47 

—  .12 

et'  ' 

+  70.8 

13 

—  .03 

—  .05 

+  66.  2 

8 

+  .03 

.00 

-f-  60.8 

29 

+  .05 

+  .04 

+  56.6 

28 

+  .03 

+  .06 

+  49.7 

25 

+  .07 

+  .10 

+  45.2 

27 

+  .23 

+  .10 

-f-  39.5 

26 

—  .12 

+  .10 

+  3:5.0 

31 

—  .19 

+  .03 

+  27.4 

47 

—  .06 

—  .03 

+  21.  1 

57 

—  .03  . 

—  .11 

+  14.6 

58 

—  .12 

—  .16 

+  9.1 

86 

—  .26 

—  .19 

+  4.1 

33 

—  .15 

-  .20 

—  1.7 

52 

—  .16 

—  .16 

—  8.7 

45 

—  .08 

—  .06 

—  14.1 

17 

+  .03 

+  .07 

—  18.9 

12 

+  .35 

+  .24 

—  21.9 

13 

+  .21 

+  .41 

—  27.9 

16 

+  .76 

+  .62 

The  outstanding  residuals  are  first  corrected  for  the  effect  of  terms  in  a,  as  found 
for  the  entire  Paris  series.    (See  Ps  56.) 
With  m  =  7,  we  have : — 

E  =  ±  ".35. 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +5° 

—  30°  to  +40° 

-f-40°  to  +90° 

—  30°  to  +90° 

Mean  a 

if 

rj 

is1 

ro' 

it1 

ro' 

?r' 

'o' 

A. 

II 

// 

// 

// 

1 

10 

—  .05 

47 

.00 

26 

+  .08 

73 

+  .03 

3 

13 

+  .07 

26 

—  .10 

11 

+  .32 

37 

+  .02 

5 

15 

+  .25 

44 

+  .16 

12 

+  .21 

56 

+  .17 

7 

4 

-j-  .50 

39 

+  .17 

1 

+  .50 

40 

+  .18 

9 

5 

.00 

35 

+  .23 

5 

—  .02 

40 

+  .20 

11 

12 

+  .25 

40 

+  .12 

24 

+  .08 

64 

+  .10 

13 

23 

+  .07 

32 

+  .0-2 

15 

—  .09 

47 

—  .02 

15 

19 

—  .04 

43 

—  .11 

24 

—  .13 

67 

—  .12 

17 

10 

—  .10 

37 

—  .14 

31 

—  .11 

68 

—  .13 

19 

19 

—  .24 

49 

—  .25 

35 

—  .15 

84 

—  .21 

21 

20 

—  .07 

50 

—  .27 

20 

—  .05 

70 

—  .20 

23 

25 

—  .02 

40 

+  .01 

8 

—  .10 

48 

.00 

For  general  explanation  sec  Ps  56. 


542 


UNITED  STATES  NOKTHEKN  BOUNDAKY  COMMISSION. 


BsGO. 

Residuals  in  order  of  declination. 


Mean  6 

TT' 

»'o 

Co 

o 

It 

// 

+  86.7 

38 

+  .21 

+  .'24 

«   „ 

+  76.6 

19 

+  .31 

+  .36 

e 

-j-  71.4 

18 

+  .64 

+  .40 

/ 

+  66.4 

7 

+  .32 

+  .39 

+  61.6 

32 

+  .53 

+  .30 

+  ">6.2 

31 

+  .03 

+  -14 

+  51.2 

43 

—  .15 

—  .11 

+  45.6 

19 

—  .47 

-  .28 

+  38.6 

32 

—  .44 

—  .31 

+  33.0 

27 

-  .20 

—  .21 

+  27.5 

57 

—  .14 

—  .04 

+  21.5 

64 

+  .11 

—  .03 

+  14.8 

65 

-  .32 

—  .08 

+  9.2 

83 

—  .01 

—  .09 

+  3.2 

38 

—  .27 

—  .05 

—  1.6 

53 

+  .10 

—  .02 

—  8.5 

45 

-  .10 

.00 

—  14.0 

24 

+  .03 

.00 

—  18.8 

14 

+  .13 

.00 

—  >;2.4 

19 

+  .21 

.00 

—  28.2 

19 

—  .25 

.00 

The  curve  from  which  Co  is  taken  is  derived  from  the  mean  of  Bs  60  and  Bs  65, 
since  there  is  no  reason  for  supposing  the  two  to  difler. 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +5° 

—  30°  to  +  40° 

+  40°  to  +  90° 

—  30°  to  +  90° 

Mean  a 

7T7 

ro' 

n1 

'V 

TT' 

ro' 

w> 

»o' 

ft. 

„ 

,1 

// 

// 

1 

11 

—  .05 

47 

—  .16 

29 

+  .01 

76 

—  .10 

3 

18 

—  .24 

30 

+  .07 

8 

+  .20 

38 

+  .10 

5 

18 

+  .31 

50 

+  .16 

12 

—  .08 

62 

+  -11 

7 

11 

+  .75 

46 

+  .40 

6 

+  .60 

52 

+  .42 

9 

7 

—  .10 

33 

—  .09 

18 

+  .12 

51 

—  .02 

11 

15            4.  .05 

43 

+  .05 

18 

—  .31 

61 

—  .05 

13 

28            —  .28 

40 

—  .17 

14 

—  .39 

54 

—  .23 

15 

18            —  .14 

54 

—  .22 

14 

—  .32 

68 

—  .24 

17 

12            —  .40 

49 

—  .28 

25 

+  .09 

74 

—  .16 

19 

16            +  .13 

53 

—  .07 

20 

—  .17 

73 

—  .10 

21 

20            +  .04 

46 

—  .02 

34 

+  .09 

80 

+  .03 

23 

20 

+  .15 

46 

-   .12 

12 

—  .12 

58 

—  .12 

There  is  n  tolerably  well-marked  correction  indicated,  which  is  substantiated  by 
the  examination  of  Bs  65.  From  the  combined  values  of  r0'  in  the  limits  —30°  to 
-f  90°,  we  have  :— 

-  (".17  ±  ".03)  sin  a  +  (".005  ±  ".03)  cos  a. 


[137J  EEPOET  OF  THE  CHIEF  ASTEONOMER,  APPENDIX  H.          543 


This  is  very  nearly  what  might  have  beeii  predicted  from  the  discussion  of  Brad- 
ley's  declination,  the  zenith-points  at  Brussels  being  derived  from  a  standard  catalogue 
of  a  much  earlier  epoch,  with  proper  motions  computed  from  the  Fundamenta. 

Correcting  the  values  of  r  for  the  curve  and  the  above  formula,  with  m  =  8,  we 
have  for  Bs  60  :— 

E  =  ±  ".59, 

Me  62. 
Residual*  in  order  of  declination. 


Meau  A 

vr' 

n> 

Co 

o 

n 

// 

+  48.6 

3 

—  1.77 

p       _ 

+  45.4 

5 

—    .99 

1  =  2 

+  38.7 

4 

+    .98 

+  .49 

ei 

+  32.4 

10 

+    .58 

+  .44 

+  27.1 

25 

+    .54 

+  .40 

+  21.0 

28 

+    .36 

+  .38 

-j-  14.7 

37 

+    .22 

+  .38 

+    9.2 

39 

+    .35 

+  .56 

+    4.2 

22 

+     .75 

+  -74 

—    1.2 

81 

+  1.13 

+  .88 

—    8.  5 

24 

+     .83 

+  .87 

—  14.0 

15 

+     .48 

+  .77 

—  18.  6 

11 

+  1.33 

+  .66 

—  22.  C 

12 

•j.    .90 

+  .57 

—  28.2 

14 

+     .33 

-j-  .46 

—  34.8 

2 

+     .52 

+  .21 

—  41.1 

1 

—    .08 

+  .06 

—  50.1 

2 

—    .12 

—  .04 

—  59.4 

6 

—    .30 

—  .20 

—  75.1 

3 

—    .19 

—  .14 

The  correction  here  determined  is  applicable  in  addition  to  the  correction  given 
in  Introduction  to  Williamstown,  1861-'63  (pp.  xxi  and  xxii). 
With  m  =  6,  we  have : — 

E  =  ±  ".90. 

This  large  probable  error,  nearly  twice  that  of  Me  68,  found  in  precisely  the  same 
way,  may  be  partly  owing  to  the  neglect  of  correction  proceeding  according  to  a.  The 
observations  themselves  are  known  to  be  less  exact*  than  those  of  Me  68,  but  appar- 
ently not  in  the  ratio  indicated  above. 

In  the  comparison  of  Gh  57  —  Me  62t  Dr.  Gylden  finds : — 

+  ".07  cos  a  +  ".14  sin  a  —  ".40  cos  2  a  —  ".34  sin  2  a. 

Something  like  this  is  indicated  in  the  examination  below,  and  probably  has  a  real 
existence.  On  the  whole,  I  thought  it  not  advisable  to  investigate  the  correction,  what- 
ever it  is,  depending  on  a. 


•  Fide  V.  J.  S.,  vol.  v,  p.  289. 


tI6W.,p.291. 


544 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 
Residuals  in  order  of  right  ascension. 


[138J 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +  5° 

+  5°  to  +  40° 

—  30°  to  +  40° 

Mean  a 

*• 

•V 

7T1 

ro' 

tt> 

ra' 

ft. 

// 

II 

II 

1 

1 

—  .17 

19 

—  .08 

26 

—  .10 

3 

11 

—  .20 

3 

—  .30 

14 

—  .24 

5 

16 

+  .18 

26 

—  .64 

42 

—  .33 

7 

8 

+  .10 

18 

—  .13 

26 

—  .06 

9 

4 

+  .10 

14 

+  .15 

18 

+  .14 

11 

10 

-f  .12 

14 

+  .41 

24 

+  .29 

13 

14 

+  .69 

2 

+  .60 

16 

+  .65 

15 

9 

+  .28 

10 

+  .92 

19 

+  .62 

17 

C 

—  .70 

12 

—  .19 

18 

—  .36 

19 

7 

—  .05 

14 

—  .25 

21 

—  .31 

21 

12 

+  .37 

10 

+  .29 

22 

—  .07 

23 

18 

+  .19 

10 

+  .12 

28 

+  .16 

Wn  64. 

The  weights  (n1)  are  constructed  as  explained  in  Section  V. 
Residuals  in  order  of  declination. 


Mean  <5 

7!-' 

ro' 

Co 

o 

// 

// 

+  87.1 

95 

+  .10 

+  .10 

+  76.1 

56 

+  .26 

+  .11 

+  70.7 

51 

+  .27 

+  .08 

+  66.1 

38 

—  .03 

+  .06 

+  62.0 

43 

—  .41 

+  .03 

+  50.2 

19 

—  .or 

—  .01 

+  50.6 

26 

+  .32 

—  .05 

+  45.7 

22 

+  .11 

—  .09 

+  38.8 

24 

+  .08 

—  .14 

+  33.0 

11 

—  .04 

—  .21 

-f  27.4 

59 

—  .33 

—  .29 

+  21.4 

67 

—  .44 

—  .38 

+  14.5 

79 

—  .31 

—  .45 

-j-  8.9 

80 

—  .59 

—  .46 

+  4.5 

38 

—  .44 

—  .44 

—  1.3 

40 

—  .11 

—  .39 

—  8.8 

37 

—  .38 

—  .29 

—  13.9 

15 

—  .60 

—  .21 

—  18.9 

8 

-f  -4 

—  .12 

—  21.4 

5 

+  .0 

—  .07 

—  28.  a 

15 

—  .1 

+  .06 

Correcting  the  outstanding  residuals  by  the  formula  embracing  terms  in  «  (see 
Wn  47)  and  with  m  =  6,  we  have: — 

J?=  ±  ".71. 


[139]  EEPOET  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  545 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +5° 

—  30°  to  +40° 

+  40°  to  +  90° 

—  30°  to  -f-  90° 

Mean  a 

m1 

*•„' 

TT' 

r,' 

W 

r0' 

7T7 

ro' 

h. 

II 

II 

// 

// 

1 

3 

—  .50 

50 

—  .19 

62 

—  .05 

112 

—  .12 

3 

8 

—  .25 

22 

—  .12 

8 

—  .36 

30 

—  .18 

5 

11 

+  .04 

36 

—  .53 

17 

—  .03 

53 

—  .37 

7 

2 

—  .20 

29 

—  .24 

11 

—  .50 

40 

—  .31 

9 

2 

+  .20 

29 

+  -17 

10 

+  .48 

39 

+  .25 

11 

6 

—  .20 

35 

—  .16 

29 

—  .32 

64 

—  .23 

13 

20 

+  -47 

34 

+  .32 

32 

+  .28 

66 

+  .30 

15 

16 

+  .33 

45 

+  .40 

48 

+  .25 

93 

+  .31 

17 

12 

+  .10 

41 

+  .34 

32 

+  .26 

73 

-f  .30 

19 

12 

—  .37 

54 

—  .08 

31 

—  .37 

85 

—  .19 

21 

20 

+  .21 

41 

—  .02 

45 

+  .23 

86 

+  .H 

83 

30 

—  .09 

51 

+  .05 

25 

—  .06 

76 

+  .01 

The  general  explanation  is  given  under  Wn  47. 

Gh  64. 
Residuals  in  order  of  declination. 


Mean  6 

71-' 

ra 

Co 

0 

H 

II 

+  86.7 

47 

+  -11 

.00 

«•      0 

+  76.5 

41 

—  .23 

.00 

—  =  O 

£ 

+  70.7 

47 

—  .12 

.00 

1 

+  66.4 

41 

+  .06 

.00 

+  61.4 

54 

+  .07 

.00 

+  55.9 

28 

—  .14 

.00 

+  51.0 

53 

+  .20 

.00 

+  45.6 

53 

—  .12 

.00 

+  40.2 

68 

+  .12 

.00 

+  32.8 

55 

—  .03 

+  .07 

+  27.2 

87 

+  .16 

+  .12 

+  21.1 

101 

+  .13 

+  .15 

+  14.6 

102 

+  .15 

+  .12 

+  8.9 

122 

+  .05 

+  .05 

+  4.2 

50 

+  .19 

.00 

-  1.2 

64 

—  .22 

—  .09 

—  8.6 

65 

—  .07 

—  .03 

-  14.1 

26 

+  .07 

+  .H 

—  18.8 

17 

+  .61 

+  .24 

—  22.1 

21 

+  .25 

+  .32 

—  28.1 

23 

+  .55 

+  .49 

With  m  =  5,  we  have : — 


E  =  ±  ".49. 


".48  is  adopted  for  the  definitive  weights,  as  explained  under  Gh  57. 
N  B 35 


546 


UNITED  STATES  NOETHEEN  BOUNDAEY  COMMISSION. 

Residuals  in  order  of  right  ascension. 


[140J 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°to  +  5° 

—  30°  to  +40° 

—  30°  to  +  90° 

Mean  a 

7T7 

»V 

a1 

n>' 

TT' 

rj 

h. 

it 

II 

II 

1 

11 

+  .57 

76 

+  .14 

114 

+  .05 

3 

16 

+  .09 

37 

—  .09 

54 

—  .01 

5 

25 

—  .01 

73 

+  .03 

104 

+  .04 

7 

7 

—  .49 

68 

—  .15 

77 

—  .13 

9 

7 

—  .40 

58 

—  .14 

76 

—  .02 

11 

21 

—  .14 

60 

—  .05 

91 

—  .11 

13 

33 

—  .14 

49 

—  .12 

79 

—  .05 

15 

28 

—  .06 

76 

+  .01 

116 

—  .03 

17 

9 

.00 

61 

+  -11 

103 

+  .09 

19 

22 

+  .02 

78 

-  .02 

121 

-.06 

21 

27 

+  .23 

69 

+  .18 

138 

+  .14 

23 

33 

+  .05 

00 

+  .13 

85 

+  .04 

For  remarks  see  Bn  66. 


Ps  64. 
Residuals  in  order  of  declination. 


Mean  <5 

TT' 

'•o 

Co 

o 

// 

// 

+  86.6 

20 

—  .18 

—  .22 

C          - 

+  76.6 

12 

—  .40 

—  .26 

—  =2 

P 

+  70.7 

11 

—  .16 

—  .27 

/ 

+  66.2 

8 

—  .04 

—  .27 

+  61.1 

21 

—  .30 

—  .25 

+  56.3 

21 

—  .17 

—  .22 

+  50.6 

30 

—  .17 

—  .22 

+  45.3 

25 

—  .33 

—  .26 

+  39.5 

25 

—  .39 

—  .30 

+  32.8 

33 

—  .31 

—  .28 

+  27.2 

47 

—  .15 

—  .16 

+  21.  0 

56 

—  .03 

-  .06 

+  14.6 

53 

—  .06 

—  .07 

+    9.1 

77 

—  .21 

—  .16 

+    4.0 

25 

—  .29 

—  .22 

-    1.8 

51 

—  .16 

—  .21 

—    8.5 

40 

—  .15 

—  .13 

—  14.1 

15 

+  .02 

+  .04 

—  18.9 

10 

+  .41 

+  .29 

—  21.9 

13 

—  .08 

+  .43 

—  27.9 

15 

+1.01 

+  .90 

With  the  correction  depending  on  a,  and  with  m  =  9,  we  have  :- 

E  =  ±  ".37. 

From  Ps  66,  we  have  :— 

E  =  ±  ".41. 

The  mean  is  adopted,  since  both  series  are  essentially  the  same. 


[141]  REPOET  OF  THE  CHIEF  ASTEONOMEE,  APPENDIX  H.  547 

Residuals  in  order  of  riglit  ascension. 


Declination  limits. 

Declination  limits. 

Declination  Iimit8. 

Declination  limits. 

—  30°  to  +  5° 

—  30°  to  +  40° 

+  40°  to  +  1)0° 

—  30°to  +  90° 

Mean  a 

If' 

ro' 

«•' 

rtf 

If1 

ro' 

«•' 

ro' 

li. 

,1 

II 

// 

// 

1 

8 

-  .25 

42 

+  .04 

25 

+  .14 

67 

+  .08 

3 

12 

+  .13 

24 

+  .05 

13 

+  .05 

37 

+  .05 

5 

16 

+  .38 

45 

+  .19 

9 

—  .07 

54 

+  -14 

7 

4 

+  .60 

40 

+  .13 

1 

+  .30 

41 

+  -14 

9 

5 

+  .20 

36 

+  .08 

8 

+  .30 

44 

+  -12 

11 

10 

+  .22 

37 

-.01 

23 

+  .16 

60 

+  .05 

13 

23 

—  .10 

32 

—  .03 

14 

+  .03 

46 

-.01 

15 

20 

+  .03 

42 

—  .15 

15 

—  .09 

57 

—  .14 

17 

10 

—  .06 

34 

—  .15 

15 

—  .17 

49 

—  .16 

19 

13 

—  .05 

48 

—  .27 

12 

—  .24 

60 

—  .27 

21 

21 

+  .05 

39 

—  .19 

17 

—  .01 

56 

—  .14 

83 

16 

—  .08 

32 

+  .50 

4 

.00 

36 

+  .04 

The  correction  is  derived  under  Ps  56. 

Bs65. 

Residuals  in  order  of  declination. 


Mean  6 

7T 

rt 

Co 

o 

n 

II 

+  87.0 

22 

+  .27 

+  .24 

f   „ 

+  76.6 

18 

+  .22 

+  .36 

-  =  3 

ff 

+  70.5 

9 

+  .47 

+  .40 

+  67.3 

1 

+  .f5 

+  .39 

+  61.8 

16 

+  .37 

+  .31 

-f  55.9 

17 

—  .01 

+  .10 

+  50.2 

30 

—  .06 

—  .17 

+  45.2 

21 

—  .22 

—  .29 

-f  39.0 

26 

—  .30 

—  .31 

-f  32.5 

26 

+  .12 

—  .19 

+  27.4 

51 

—  .05 

—  .03 

+  21.3 

47 

+  .27 

+  .0:J 

+  14.4 

48 

—  .08 

—  .08 

+  8.8 

67 

+  .07 

—  .09 

+  4.2 

27 

+  .14 

—  .05 

—  1.6 

47 

—  .12 

—  .02 

—  8.6 

42 

+  .02 

.00 

—  14.0 

22 

+  .26 

.00 

—  18.8 

15 

+  .15 

.00 

—  22.3 

18 

+  .13 

.00 

—  28.2 

8 

—  .05 

.00 

From  the  final  residuals,  corrected  as  in  the  case  of  Bs  60,  we  have  (with  m  =  8): — 

E  =  ±  ".44. 

I  have  considered  this  large  increase  in  precision  to  be  real,  and  have  adopted  the 
respective  values  of  E,  as  determined,  in  constructing  the  definitive  table  of  weights 
lor  Bs  CO  and  Bs  65. 


548  UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.          [142] 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +5° 

—  30°  to  +40° 

4.  4QO  to  _j_  goo 

—  30°  to  +90° 

Mean  a 

7T7 

rj 

•K1 

rd 

n1 

tV 

TT' 

r»' 

h. 

a 

it 

n 

// 

I 

11 

+  .35 

43 

+  .16 

20 

—  .09 

63 

+  .08 

3 

13 

+  .55 

23 

+  .39 

7 

+  .10 

30 

+  .32 

5 

13 

+  .12 

37 

+  .35 

7 

+  .13 

44 

+  .32 

7 

5 

+  .50 

28 

+  .32 

3 

+  .20 

31 

+  .31 

9 

7 

.00 

28 

+  .14 

10 

+  .29 

38 

+  .18 

11 

12 

+  .12 

36 

+  .20 

18 

+  .26 

54 

+  .23 

13 

26 

—  .20 

38 

—  .06 

10 

+  .10 

48 

—  .03 

15 

20 

+  .04 

41 

.00 

13 

+  .07 

54 

+  .01 

17 

10 

—  .06 

44 

—  .04 

15 

—  .11 

59 

-.06 

19 

13 

—  .05 

45 

—  .18 

7 

+  .19 

52 

—  .13 

21 

21 

+  .05 

43 

+  .05 

19 

-.07 

62 

+  .01 

23 

16 

-  .08 

34 

.00 

8 

—  .34 

42 

-.06 

For  farther  explanations  see  Bs  CO. 

Ps  66. 
Residuals  in  order  of  declination. 


Mean  6 

7T7 

n> 

Co 

o 

// 

II 

+  87.4 

16 

—  .32 

—  .20 

e 

+  76.7 

7 

—  .10 

—  .20 

7=2 

+  70.9 

5 

—  .15 

—  .18 

c/ 

+  G6.0 

5 

—  .19 

—  .12 

+  60.9 

19 

+  .01 

—  .03 

+  56.5 

19 

+  .07 

.00 

+  f>0.4 

20 

+  -14 

-  .01 

+  45.2 

27 

—  .13 

—  .07 

+  39.4 

26 

—  .26 

—  .15 

+  32.9 

34 

—  .19 

—  .16 

+  27.4 

47 

—  .06 

—  .10 

+  21.2 

51 

—  .03 

—  .06 

+  14.7 

52 

-  .11 

—  .16 

+    9.1 

78 

—  .29 

—  .25 

+    4.1 

26 

—  .32 

—  .27 

—    1.8 

43 

—  .21 

—  .24 

—    8.5 

41 

—  .25 

—  .19 

—  14.1 

14 

+  .01 

—  .09 

—  18.7 

12 

—  .14 

+  .02 

—  21.9 

12 

+  -11 

+  -14 

—  27.9 

15 

+  .56 

+  .39 

In  the  same  manner  as  with  Ps  64,  we  have : — 

H  =  ±  ".41. 
.39  is  adopted,  as  previously  explained. 


[143  REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.  549 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +  5° 

—  30°  to  +  40° 

+  40°  to  +  90° 

—  30°  to  +90° 

Mean  a 

TT' 

«'o' 

T 

n,' 

TT' 

ro' 

K» 

ro' 

*. 

// 

II 

It 

// 

1 

8 

+  .35 

45 

—  .08 

18 

+  .18 

63 

.00 

3 

10 

—  .22 

22 

—  .21 

13 

+  .18 

35 

—  .07 

5 

16 

+  .10 

42 

+  .26 

8 

+  .05 

50 

+  .26 

7 

3 

+1.40 

36 

+  .28 

0 

.00 

36 

+  .28 

9 

4 

+  .30 

33 

+  .11 

8 

—  .07 

41 

+  .08 

11 

10 

+  .52 

32 

+  .24 

16 

+  .12 

48 

+  .20 

13 

22 

+  .14 

31 

+  .10 

11 

+  .37 

42 

+  .17 

15 

16 

—  .15 

40 

—  .17 

12 

+  .27 

52 

—  .07 

17 

9 

+  .39 

35 

—  .20 

9 

+  .02 

44 

—  .15 

19 

19 

—  .11 

45 

—  .21 

10 

—  .64 

55 

—  .29 

21 

16 

—  .08 

46 

—  .14 

16 

—  .22 

62 

—  .16 

23 

20 

+  .04 

36 

+  .03 

7 

—  .31 

43 

—  .02 

The  discussion  of  correction  is  given  under  Ps  56. 

Bn66. 
Each  value  of  r  receives  weight  one. 

Residuals  in  order  of  declination. 


Mean  6 

7T 

»'o 

Co 

o 

// 

// 

+  85.6 

2 

+  .34 

+  .41 

+  70.  3 

4 

+  .47 

+  .67 

+  71.0 

6 

+  .82 

+  -71 

+  66.1 

3 

+  .72 

+  .57 

+  62.0 

5 

+  .26 

+  .25 

+  56.0 

4 

—  .45 

—  .28 

+  50.6 

10 

—  .58 

—  .54 

+  45.4 

6 

—  .63 

—  .59 

+  39.2 

3 

—  .6-2 

—  .56 

+  32.8 

5 

—  .27 

—  .45 

+  27.0 

5 

—  .58 

—  .32 

+  20.7 

9 

—  .19 

—  .25 

+  15.0 

4 

—  .43 

—  .20 

+    9.0 

8 

.00 

—  .21 

+    4.1 

4 

—  .34 

—  .27 

-    1.3 

8 

—  .36 

—  .35 

—    8.2 

4 

—  .35 

—  .40 

—  14.0 

2 

+  .05 

—  .40 

—  18.7 

3 

—  .76 

—  .40 

—  22.5 

3 

—  .48 

—  .40 

—  28.8 

1 

[+.51] 

[-  .40] 

The  correction  in  order  of  declination,  as  well  as  right  ascension,  appears  to  re 
produce  in  proper  proportion  and  with  opposite  signs  the  peculiarities  noticed  in  the 
correction  for  Bradley's  declinations. 


550 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 
Residuals  in  order  of  right  ascension. 


[144] 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +  6° 

—  30°  to  +  40° 

+  40°  to  4-  U0° 

Mean  a 

•* 

ro' 

if 

rj 

w' 

>v 

fi. 

II 

II 

// 

1 

2 

—  .30 

6 

—  .20 

5 

+  .14 

3 

2 

+  .25 

4 

+  .37 

2 

4-  .10 

5 

3 

+  .13 

6 

4-  .07 

4 

+  .08 

7 

2 

4-  .CO 

5 

4-  .48 

9 

3 

+  .03 

4 

+  .12 

11 

2 

-f  .65 

6 

4-  .57 

4 

—  .33 

13 

4 

-f-  -07 

6 

.00 

2 

+  .25 

15 

2 

—  .55 

4 

—  .45 

4 

—  .30 

17 

1 

—  .30 

4 

-  .10 

5 

—  .14 

19 

2 

—  .64 

4 

—  .31 

2 

+  .90 

21 

1 

+  .10 

5 

—  .32 

6 

—  .30 

23 

4 

—  .10 

5 

—  .06 

3 

—  .03 

The  "Northern  stars"  were  reduced  on  other  principles  than  those  adopted  for  the 
zone  —30°  to  +  40°.  Argelander  has  given  (in  Volume  VI.  of  the  V.  J.  S.  derAst.  Oes., 
p.  100)  the  results  of  a  very  careful  comparison  of  the  difference  of  declination  between 
Gh  64  and  Bu  GG.  He  finds  (p.  114,  ibid)  for  the  zone  -  30°  to  +  40°:— 

(1;  —  ".425  +  0".313  sin  a  —  0".201  cos  a, 

as  the  difference  "Gr.  —  Bonn."  From  the  above  table,  declination  limits  —30°  to 
+  400,  I  find  :_ 

(2)  +  0".309  sin  a  —  0".151  cos  a, 

as  the  correction  to  Bn  66.  This  coincidence  between  the  periodic  terms  of  (1)  and  (2) 
tends  to  prove  that  the  discrepancy  between  Gh  64  and  Bn  66  is  almost  wholly  due  to 
error  of  the  latter. 

Taking  the  mean  epoch  of  the  catalogues  upon  which  are  based  the  declinations  of 
Wolfer's  Tabulce  Reductionum  (also  Berlin  Jahrbuch,  on  which  Argelander's  (1866)  decli- 
nations are  founded)  to  be  1832,  and  assuming  their  mean  to  be  practically  free  from 
error,  proceeding  according  to  right  ascension,  we  shall  have  as  the  correction  to  these 
declinatious  (Berlin  Jahrbvch)  for  18GG,  and  for  +  20°  declination: — 


x  (+  ".84  sin  a  +  ".17  cos  a)  •. 


+  ".37  sin  a  +  ".06  cos  a.* 


Considering  the  great  uncertainty  of  the  individual  positions  of  Wolfer'a  catalogue 
for  1866,  this  may  be  regarded  as  a  very  fair  approximation  to  (2),  which  is  adopted  as 
the  definitive  correction  for  the  zone  —  30°  to  +  40°.  The  Northern  stars  appear  to 
require  no  such  correction. 

With  m  =  8,  we  have : — 

E  =  ±  ".31. 


*  Argelander  finds  (V.  J.  S.,  Vol.  V.,  p.  110.)  Gr.  1864  —  Wolfer's==  +  0".475  sin  (a  —  2°  58'.) 


[145] 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


551 


Re  66. 

Owing  to  the  extreme  uncertainty  of  the  individual  corrections,  the  comparisons 
with  definitive  curves  are  of  little  interest,  and  for  convenience  they  are  here  omitted. 
The  residuals  were  all  plotted  on  a  single  sheet,  so  that  peculiarities  common  to  all  the 
years  were  easily  detected. 

Residuals  in  order  of  declination. 


Meand 

Re  62. 

Re  63. 

Re  64. 

Re  65. 

Re  60. 

Re  67. 

Re  68. 

Re  69. 

* 

ra 

V1 

fa 

ir7 

TO 

nf 

n> 

•K> 

r<> 

TT' 

»0 

*? 

ra 

TT' 

TO 

o 

H 

it 

it 

ii 

11 

II 

it 

ii 

+  87 

34 

—  .25 

38 

—  .  12 

34 

+  .33 

27 

+  .21 

22 

+  .84 

20 

+  .16 

33 

+  .08 

36 

+  .05 

+  "« 

12 

—  .63 

8 

—1.41 

18 

+  .32 

8 

+  .<J4 

8 

+1.46 

81 

—  .01 

1? 

+  .05 

21 

—  .04 

+  70 

5 

+  .00 

8 

—  .55 

9 

—  .42 

4 

+  1.30 

8 

+1.36 

•21  i 

+  .15 

28 

+  .74 

41 

—  .03 

+  65 

2 

—  .15 

4 

+  .30 

5 

+  .53 

2 

+  1.40 

0 

+  .07 

8 

—  .47 

17 

—  .48 

+  62 

5 

—1.53 

4 

—1.60 

17 

1        •  "v 

—1.09 

18 

+  .12 

4 

+  I.CO 

20 

|            I    V» 

—  .10 

81 

+  .02 

39 

—  .16 

_j_  50 

1 

—3.10 

7 

—  .93 

1 

+1.00 

3 

+  .80 

11 

—  .17 

23 

+  .34 

49 

—  .10 

4-  r>i 

6 

—1.60 

1 

—1.00 

6 

1    *•  vv 

—  .32 

5 

+1  90 

17 

—  .82 

10 

r  * 
—  .16 

36 

—  .46 

r   * 

+  45 

5 

—  1.50 

1 

+  .60 

2 

-1.10 

3 

+1.03 

9 

—  j—  *.   v  v 

+  .14 

6 

—1.03 

6 

+1.26 

22 

—  .44 

-j-  39 

4 

—  1.45 

6 

4-  .05 

7 

—  .37 

<J 

—  .63 

14 

—  .55 

10 

—  .40 

32 

—  .22 

+  32 

17 

—1.77 

13 

—  |—      .   \J  *r 

—  .37 

10 

—  .55 

20 

—  .53 

84 

—  .43 

19 

—  .62 

7 

—  .01 

24 

—2.75 

+  27 

02 

—1.31 

41 

—  .61 

33 

—  .60 

34 

+  .02 

41 

—  .05 

33 

—  .29 

so 

+  .12 

52 

—  .29 

+  21 

44 

—  1.  51 

52 

-1.15 

32 

—  .48 

27 

+  .14 

11 

—  .56 

38 

—  .51 

31 

+  .12 

34 

—  .37 

.+  15 

58 

—1.78 

56 

—1.32 

24 

—  .48 

43 

—  .40 

•11 

—  .88 

38 

—  .26 

87 

—  .15 

54 

—  .65 

+    9 

56 

—1.80 

63 

—1.16 

33 

—  .49 

54 

—  .44 

68 

—  1.  2(> 

40 

—  .98 

89 

+  .07 

54 

—  .55 

+    4 

30 

—1.44 

28 

—  .37 

24 

+  .43 

26 

—  .16 

19 

—  .67 

12 

—1.80 

10 

—1.14 

18 

—  .58 

31 

—  .85 

40 

+  .15 

24 

+  .07 

23 

+  .22 

80 

—1.16 

14 

—  .67 

16 

—  .71 

27 

—  .70 

—    8 

34 

—  .61 

31 

—  .27 

18 

+  .86 

30 

+  .46 

21 

—  .5<i 

IS 

—  .83 

14 

—  .64 

19 

—  .24 

—  14 

12 

—  .38 

18 

—  .21 

8 

+  .58 

15 

+  .55 

13 

—1.04 

1 

+  .60 

3 

+  .43 

10 

—  .25 

—  19 

10 

+  .01 

10 

—  .16 

6 

—  .45 

9 

+  .72 

10 

—1.80 

6 

—1.18 

4 

—1.02 

7 

—  .67 

—  22 

11 

—  .63 

16 

+  .14 

7 

+  .46 

8 

—  .47 

10 

—1.96 

2 

—1.80 

3 

+  .30 

7 

—  .57 

—  28 

10 

+2.85 

7 

+  .83 

4 

+  .18 

7 

+  .06 

4 

—2.67 

6 

—2.79 

8 

—  .66 

10 

+  .15 

For  the  earlier  years  the  curve  of  correction  for  stars  from  +  35°  to  +  90°  is 
necessarily  largely  ideal. 

With  various  values  of  «i,  I  deduce  roughly. 

E  =  ±  I'M. 

From  Re  72,  we  have : — 

E  =  ±  ".9. 

The  mean  ±  1".00  is  adopted  in  forming  the  definitive  table  of  weights. 


552          UNITED  STATES  NORTHERN    BOUNDARY  COMMISSION.         [146 1 

Besidtials  in  order  of  right  ascension. 


Re  62. 

Ee63. 

EeG4. 

Re  65. 

Re  66. 

Re  67. 

Re  68. 

Re  69. 

Ttf 

ill  run  a 

V 

ro' 

jr1 

»-o' 

* 

*•„' 

TT' 

r,' 

JT' 

>•<>' 

V 

»•„' 

ir1 

»V 

«•' 

»•„' 

h. 

II 

it 

II 

n 

II 

II 

// 

II 

i 

37 

+  .18 

37 

—  .11 

38 

—  .25 

44 

+  .53 

40 

+  .05 

33 

—  .04 

40 

—  .19 

61 

+  .17 

3 

18 

—  .04 

21 

—  .30 

11 

+  .04 

16 

+  .24 

19 

+  .22 

21 

—  .89 

H 

—  .29 

18 

+  .28 

5 

37 

+  .29 

31 

—  .18 

12 

-  .CO 

22 

-  .06 

.-,() 

+  .18 

26 

—  .19 

86 

+  .79 

21 

+  .13 

7 

32 

+  -41 

36 

+  .30 

22 

—  .39 

21 

—  .36 

36 

—  .43 

30 

—  .19 

88 

+  .67 

24 

—  .28 

9 

27 

+  .52 

26 

—  .50 

19 

—  .07 

14 

+  .13 

11 

—  .02 

16 

+  .35 

1! 

-  .05 

39 

—  .10 

11 

26 

+  .09 

34 

—  .24 

28 

—  .25 

27 

—  .03 

93 

—  .12 

38 

+  .37 

:*7 

+  .39 

57 

—  .05 

13 

27 

+  .06 

30 

+  .28 

17 

—  .25 

17 

—  .21 

21 

+  .12 

30 

+  .03 

81 

—  .04 

52 

+  .20 

15 

r.2 

—  .11 

45 

+  .10 

31 

+  .15 

44 

—  .02 

:!~ 

+  .18 

44 

+  .27 

46 

—  .06 

69 

+  .11 

17 

39 

—  .65 

45 

+  -17 

15 

+  .77 

31 

—  .98 

46 

—  .25 

46 

+  .06 

43 

+  .OS 

88 

-  .06 

19 

51 

—  .48 

43 

+  .34 

33 

+  .31 

37 

—  .66 

38 

—  .58 

35 

+  .12 

30 

—  .28 

74 

—  .15 

21 

54 

+  .13 

52 

—  .07 

£0 

—  .19 

53 

+  .17 

;;i 

+  .19 

32 

-  .39 

38 

—  .21 

56 

+  .16 

23 

34 

—  .04 

39 

+  .32 

37 

+  .50 

41 

+  .44 

80 

+  .31 

25 

—  .08 

2-2 

—  .88 

46 

+  .11 

There  appears  to  be  no  consistent,  well-defined  correction  depending  on  A.  R.    The 
division  into  zones  proved  equally  unavailing  for  the  discovery  of  such  a  correction. 

Lc67. 
Each  value  of  r  receives  weight  one. 

Residuals  in  order  of  declination. 


Mean  <5 

7T7 

ra 

Co 

o 

H 

II 

+  86.7 

5 

+    .38 

+  .38 

+  76.8 

4 

+    .82 

+  .87 

+  71.0 

6 

+  1.20 

+  .99 

+  66.4 

5 

+  1.18 

+  .93 

+  60.8 

13 

+    .89 

+  .74 

+  56.5 

8 

+    .36 

+  .52 

+  50.9 

14 

.00 

+  .23 

+  45.6 

11 

—    .23 

—  .01 

+  40.1 

11 

+     .10 

—  .23 

+  33.3 

8 

—     .09 

—  .40 

+  27.5 

9 

—    .49 

—  .50 

+  21.2 

10 

—    .81 

—  .55 

+  15.5 

11 

—    .48 

—  .53 

+    8.8 

13 

-     .33 

—  .46 

+    4.0 

7 

—    .35 

—  .43 

—    1.7 

11 

—    .54 

—  .43 

—    8.6 

7 

—    .51 

—  .43 

—  14.0 

2 

—    .32 

—  .40 

—  18.7 

3 

.00 

—  .32 

—  22.5 

3 

—    .32 

—  .24 

—  28.8 

1 

—    .40 

—  .08 

With  m  —  8,  we  have  :— 


E  =  ±  ".27. 


[147] 


EEPOET  OP  THE  CHIEF  ASTBONOMEE,  APPENDIX  H. 

Residuals  in  order  of  right  ascension. 


553 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +  5° 

—  30°  to  +40° 

—  30°  to  +90° 

Mean  a 

it 

»o' 

* 

»•„' 

*> 

ro' 

ft. 

// 

II 

a 

1 

2 

—  .05 

10 

.00 

18 

—  .03 

3 

3 

+  .07 

5 

+  .12 

8 

-  .04 

5 

4 

+  .25 

10 

+  .14 

17 

+  .16 

7 

2 

.00 

7 

+  .01 

8 

-  .01 

9 

1 

.00 

5 

+  .22 

10 

+  .06 

11 

3 

+  .10 

8 

.00 

17 

—  .15 

13 

5 

—  .23 

7 

—  .33 

10 

—  .12 

15 

2 

+  .05 

7 

+  .14 

14 

+  .04 

17 

1 

+  .10 

7 

+  .21 

15 

+  .16 

19 

3 

+  .20 

10 

+  .07 

18 

+  .04 

21 

2 

—  .30 

8 

+  .09 

16 

+  .02 

23 

4 

—  .20 

3 

-.19 

12 

-.14 

Ln  67. 
Each  value  of  r  receives  equal  weight. 

Residuals  in  order  of  declination. 


With  m  =  4,  we  have : — 


E=  ±".137. 


Mean  <! 

TT' 

ro 

Co 

o 

it 

// 

+  86.7 

5 

±  .00 

.00 

+  76.8 

3 

+  .04 

—  .01 

+  69.9 

1 

-  .22 

—  .05 

+  66.3 

3 

—  .16 

—  .09 

+  60.7 

10 

—  .23 

—  .16 

+  56.  4 

7 

—  .20 

—  .21 

+  51.1 

13 

—  .25 

—  .24 

+  45.6 

10 

—  .33 

—  .26 

+  40.0 

11 

—  .09 

-  .26 

+  33.6 

5 

—  .26 

—  .26 

+  27.2 

8 

—  .21 

—  .26 

+  20.7 

7 

—  .40 

—  .26 

+  14.5 

9 

—  .22 

—  .24 

+    8.6 

11 

—  .37 

—  .22 

+    3.9 

5 

—  .19 

—  .16 

—    2.2 

6 

+  .06 

—  .09 

—    8.6 

6 

+  .17 

+  .01 

—  14.1 

3 

-  .14 

+  .09 

The  weight  (on  the  adopted  scale)  from  this  value  of  E  is  4.8  As  the  fundamental 
and  circumpolar  stars  are,  without  doubt,  more  exactly  determined  than  others  at  Lei- 
den, to  them  in  definitive  discussion,  is  assigned  weight  5.0,  and  to  all  others  weight 
4.0. 


554 


UNITED  STATES  SOUTHERN  BOUNDARY  COMMISSION. 

Residuals  in  order  of  right  ascension. 


[148] 


Declination  limits. 
—  30°  to  +5° 

Declination  limits. 
—  30°  to  +  40° 

Declination  limits. 
—  30°  to  +90° 

Mean  a 

*-' 

*' 

TT' 

'V 

n-' 

rj 

Ti. 
1 
3 
5 
7 
9 
11 
13 
15 
17 
19 
21 
23 

1 

3 
2 

// 

+  .46 
-  .22 

+  .04 

11 
4 
14 
8 
8 
6 
4 
11 
22 
16 
16 
12 

// 

—  .05 
—  .24 
+  .03 
-f-  .08 
-|-  .02 
—  .06 
+  .03 
—  .05 
—  .01 
+  .14 
+  .11 
+  .07 

28 
14 
29 
12 
14 
26 
13 
23 
39 
32 
35 
20 

// 

—  .01 
—  .02 
—  .03 

+  -11 
—  .03 
+  .01 
—  .05 
—  .01 
—  .05 
+  .07 
+  .03 
+  .06 

2 
2 
2 
3 
2 
4 
(i 
4 

+  .17 

+  .07 
+  .08 
—  .12 
—  .08 
+  .19 
+  .08 
+  .34 

Me  68. 

Residuals  in  order  of  declination. 


Mean  <t 

* 

,o 

C0 

o 

„ 

ft 

+  49.0 

2 

[+  1.8] 

+  1.2 

e 

+  45.8 

11 

+  1.1 

+  1.0 

ef 

+  38.6 

12 

+     .63 

+     .61 

+  32.3 

16 

+     .47 

+    .23 

+  27.4 

36 

+     .06 

+    .01 

+  21.1 

40 

—    .06 

—    .14 

+  14.6 

44 

—    .46 

—    .15 

+    8.8 

50 

—    .03 

—    .15 

+    4.4 

29 

—    .12 

—    .15 

—    1.3 

39 

—    .09 

—    .17 

—    8.6 

30 

—    .24 

—    .20 

—  14.4 

17 

—    .41 

—    .25 

—  18.8 

13 

—    .06 

—    .29 

—  22.  6 

16 

—    .45 

—    .31 

—  28.1 

17 

—    .33 

—    .34 

—  34.8 

2 

—    .27 

—    .38 

—  42.1 

3 

—    .48 

—    .39 

—  50.  1 

2 

+    .09 

—    .34 

—  59.2 

7 

-    .36 

—    .23 

—  75.1 

3 

—    .05 

—    .09 

With  m  =  5,  we  have : — 

E  =  ±  ".47. 
Dr.  Gylden  found,  from  the  results  of  1863-'o  :- 


* E=   /(0.26)2+  i  {0.263  +  0.0467  RlIrT] 

This  would  give  nearly  ±  ".6  as  the  probable  error  corresponding  to  E  above. 
As  it  is  probable  that  in  later  work  the  accuracy  of  observation  improved,  the 
value  for  E,  ±  ".47,  is  adhered  to. 

•  V.  J.  S.,  Bd.  IV,  s.  102. 


[149] 


EEPOET  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 

Residuals  in  order  of  right  ascension. 


555 


Declination  limits. 

Declination  limits. 

Declination  limits. 

+  5°  to—  30° 

-f  5°  to  +  30° 

—  30°  to  -f  40° 

Mean  a 

V 

rtf 

•K1 

rj 

TT' 

ro' 

ft. 

,1 

II 

// 

1 

8 

+    05 

24 

+  .15 

32 

+  .11 

3 

12 

10 

8 

+  .15 

20 

.00 

5 

16 

+   10 

24 

.00 

40 

+  .04 

7 

10 

—    15 

16 

+  .50 

26 

—  .03 

9 

4 

—    30 

12 

+  .20 

16 

+  .07 

11 

9 

-f     12 

20 

—  .10 

29 

—  .03 

13 

22 

—    02 

8 

—  .10 

30 

—  .04 

15 

20 

+    25 

20 

—  .02 

40 

—  .12 

17 

10 

+    15. 

20 

—  .14 

30 

—  .04 

19 

10 

—    10 

26 

.00 

38 

—  .03 

21 

13 

—    19 

27 

+  .06 

30 

—  .03 

23 

18 

+    02 

12 

—  .43 

30 

-  .16 

For  further  remarks  see  Section  V.,  comparison  of  Me  68  and  Wn  68. 

Wn  68. 

The  weights  are  adopted  from  the  discussion  in  Section  V. 
Residuals  in  order  of  declination. 


Mean  <J 

7T7 

fa 

C0 

o 

II 

II 

+  87.0 

405 

+  .04 

+  .01 

+  76.5 

181 

-  .02 

+  .08 

+  70.7 

172 

+  .15 

+  .14 

+  66.7 

124 

+  .10 

-f  .18 

+  62.  1 

79 

+  .34 

+  .24 

+  55.3 

66 

+  .23 

+  .32 

+  50.4 

155 

+  .42 

+  .35 

H-  45.7 

84 

+  .35 

+  .39 

+  39.1 

247 

+  .36 

+  .43 

+  33.2 

78 

+  .41 

+  .46 

+  27.6 

406 

+  .43 

+  .48 

+  21.1 

399 

+  -51 

+  .52 

+  14.5 

440 

+  .50 

+  .56 

+  8.9 

526 

+  .69 

+  .57 

+  4.2 

220 

+  .45 

+  .58 

—  1.3 

336 

+  .76 

+  .59 

—  8.7 

311 

+  .47 

+  .60 

—  14.1 

125 

+  .57 

+  .62 

—  19.1 

68 

+  .54 

4-  .69 

—  22.  5 

109 

+  .64 

+  .75 

—  27.8 

107 

-j-  .95 

+  .88 

The  values  of  ra  would  have  been  very  well  represented  by  the  correction  derived 
in  Section  V.  from  a  comparison  of  Wn  68  and  Me  68. 

I  find  :— 

E  =  ±  ".91. 

The  weights  were  constructed  on  a  unit  whose  probable  error  was  supposed  to  be 
±  T'.OO.    The  latter  value  for  E  is  adopted. 


550  UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.        [150J 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +5° 

—  30°  to  +  40° 

+  40°  to  +  90° 

—  30°  to  +  90° 

Mean  a 

7T 

r,' 

7T7 

»o' 

tf 

)•„' 

* 

ro' 

h. 

// 

// 

// 

tt 

1 

62 

—  .23 

350 

—  .05 

177 

.00 

527 

—  .03 

3 

94 

—  .56 

1(12 

—  .18 

24 

+  .54 

186 

—  .08 

5 

85 

+  .07 

307 

—  .02 

35 

—  .13 

342 

—  .03 

7 

Gd 

+  .17 

259 

+  .03 

90 

+  .16 

349 

+  .07 

9 

39 

—  .08 

2:i6 

+  .14 

49 

—  .30 

285 

+  .06 

11 

94 

+  .18 

327 

+  .07 

97 

—  .04 

424 

+  .05 

13 

193 

—  .12 

2H3 

—  .06 

118 

—  .14 

401 

—  .09 

15 

17 

130 
68 

+  .02 
+  .19 

351 
251 

+  .01 
+  .05 

181 
136 

—  .02 
.00 

532 

387 

.00 
+  .04 

19 

101 

—  .16 

296 

—  .21 

113 

+  .12 

409 

—  .12 

21 

129 

—  .12 

238 

—  .13 

219 

+  .18 

457 

+  .01 

23 

135 

+  .14 

237 

+  .11 

140 

+  .13 

377 

+  .12 

Gh  70. 
Residuals  in  order  of  declination. 


Mean  <J 

JT7 

ro 

Co 

Form. 

o 

II 

// 

n 

+  86.6 

48 

—  .15 

—  .06 

—  .05 

e 

+  76.4 

42 

—  .51 

—  .19 

—  .19 

=  3 

+  70.6 

59 

-  .09 

—  .24 

—  .24 

€t 

+  66.4 

31 

—  .04 

—  .29 

—  .26 

+  61.1 

89 

—  .31 

—  .'3 

—  .28 

+  56.6 

36 

—  .91 

—  .36 

—  .28 

+  51.1 

71 

—  .40 

—  .39 

—  .28 

+  45.6 

61 

—  .29 

—  .41 

—  .28 

+  39.8 

82 

—  .55 

—  .42 

—  .29 

+  32.9 

61 

—  .42 

—  .40 

—  .32 

+  27.3 

87 

—  .32 

—  .35 

—  .36 

+  21.1 

96 

—  .21 

—  .33 

—  .43 

+  14.6 

97 

—  .41 

—  .41 

—  .54 

+    8.9 

126 

—  .55 

—  .54 

—  .64 

+    4.3 

51 

—  .67 

—  .69 

—  .75 

—    1.7 

73 

—1.15 

—  .87 

—  .88 

—    8.7 

52 

—1.15 

—1.  15 

—1.05 

—  14.1 

19 

—1.05 

—1.38 

—1.16 

—  18.6 

15 

—1.61 

—1.60 

—1.25 

—  22.6 

20 

—1.28 

—1.80 

—1.32 

—  27.8 

19 

—2.11 

—2.1 

—1.4 

The  preliminary  correction  —  1".17  (sin  3z  -{-  sin  V)  found  from  the  fundamental 
and  circumpolar  stars  is  unusual;  column  "Form "is  therefore  computed  from  it  in 
order  to  show  its  general  agreement  with  the  definitive  curve.  A  slight  increase  of 
tho  coefficient  would  make  the  agreement  better. 

With  m  =  5,  we  have : — 

H  =  ±  ".58. 

This  increase  over  the  values  of  E  found  for  Gh  57  and  Gh  64  is  most  likely  due 
to  the  error  in  microscope  micrometers,  lately  discovered  at  Greenwich. 


[151] 


EEPOET  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 

Residuals  in  order  of  riglit  ascension. 


557 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30to+f>° 

—  30°  to  +40° 

—  30°  to  +  90° 

Mean  a 

_/ 

'o' 

5T7 

'V 

JT* 

ro' 

h. 

a 

// 

II 

1 

11 

—  .02 

74 

+  .01 

146 

—  .03 

3 

11 

+  .53 

33 

+  .23 

46 

+  -I? 

5 

24 

+  -11 

70 

—  .04 

111 

+  .02 

7 

5 

+  .88 

65 

—  .09 

74 

—  .08 

9 

7 

—  .20 

55 

+  .02 

82 

—  .01 

11 

17 

—  .14 

60 

+  .01 

121 

—  .14 

13 

33 

—  .18 

49 

—  .02 

84 

—  .08 

15 

32 

.00 

78 

+  .01 

128 

—  .13 

17 

15 

—  .17 

72 

—  .05 

133 

+  .05 

19 

23 

+  .40 

84 

+  .09 

116 

+  -11 

21 

18 

+  .02 

64 

-  .03 

129 

.00 

23 

29 

—  .33 

59 

—  .26 

84 

—  .14 

Re  72. 

The  corrections  for  this  series  of  annual  catalogues  are  determined  in  tho  came 
manner  as  those  for  Re  66. 

Residuals  in  order  of  declination. 


Mean  S 

Re  70. 

Re  71. 

Re  72. 

Re  73. 

v> 

'o 

TT' 

ra 

«* 

ft 

71"' 

>•" 

o 

II 

If 

n 

II 

+  87 

36 

+  .21 

31 

+  .27 

36 

+  .21 

34 

-t-  .20 

+  76 

22 

-  .06 

19 

+  .26 

20 

+  .30 

21 

+  .63 

+  70 

32 

+  .31 

32 

+  .38 

33 

+  .46 

30 

+  .52 

+  65 

15 

+  .22 

16 

+  .97 

19 

+  .79 

15 

+  .85 

+  62 

45 

—  .10 

46 

+  .38 

46 

+  .-10 

28 

+  .71 

+  56 

38 

+  .33 

39 

+  .r>8 

40 

+  .92 

39 

+1.09 

+  51 

35 

+  .09 

28 

+  .45 

33 

+  .42 

27 

+  .39 

+  45 

30 

+  .25 

21 

—  .01 

19 

+  .42 

17 

+  .£9 

+  39 

28 

-  .29 

21 

+  .29 

26 

+  .17 

27 

+  .08 

+  32 

31 

—  .66 

20 

—  .23 

20 

—  .29 

29 

—  .04 

+  27 

53 

—  .68 

60 

—  .29 

56 

—  .22 

53 

—  .35 

+  21 

43 

—  .56 

44 

—  .11 

48 

—  .02 

38 

+  .17 

+  15 

51 

—  .04 

51 

+  .17 

55 

+  .33 

68 

+  .22 

+  9 

60 

+  .45 

60 

+  .48 

54 

+  .46 

60 

+  .31 

+  4 

22 

—  .11 

22 

+  .85 

24 

+  .23 

19 

—  .33 

26 

—  .15 

30 

+  .14 

28 

+  .37 

31 

+  .07 

—  8 

25 

—  .46 

22 

-.04 

22 

+  .13 

18 

—  .97 

—  14 

11 

—  .90 

9 

+  .04 

10 

+  .15 

10 

—  .12 

—  19 

5 

—1.04 

6 

—  .70 

3 

+  -17 

7 

+  .02 

—  22 

6 

—  .15 

7 

+  .30 

9 

—  .32 

5 

—1.56 

—  28 

8 

—1.65 

6 

—  .38 

6 

—  .40 

9 

+  .12 

We  have:- 

E  =  ±  ".9. 

1".00  is  adopted,  as  previously  explained. 


558 


UNITED  STATES  NORTHERN   BOUNDARY  COMMISSION. 


[152] 


Residuals  in  order  of  right  ascension. 


Meau  a 

Be  70. 

Re  71. 

Re  72. 

Re  73. 

Re  62-73. 

tf 

ro' 

TT1 

ro' 

JT' 

V 

JT' 

ro' 

ro' 

A. 

If 

// 

II 

II 

II 

1 

67 

+  .03 

64 

—  .93 

58 

4  .55 

59 

+  .46 

-4-  .10 

3 

25 

+  .03 

17 

4  .49 

20 

+  .37 

22 

4  .37 

4  .01 

5 

46 

+  .55 

35 

4  .37 

36 

—  .14 

41 

4  .40 

4  .19 

7 

3d 

—  .28 

43 

—  .05 

41 

—  .15 

27 

+  .09 

—  .07 

9 

29 

—  .21 

32 

+  .24 

30 

+  .15 

26 

+  .23 

+  .03 

11 

60 

—  .09 

57 

—  .17 

48 

—  .21 

59 

-j-  .04 

—  .04 

13 

36 

—  .14 

52 

—  .02 

45 

4  .06 

35 

—  .09 

+  .04 

15 

67 

—  .27 

76 

+  .03 

66 

—  .24 

69 

—  .08 

—  .01 

17 

71 

—  .20 

55 

+  .05 

65 

—  .07 

59 

—  .46 

—  .12 

19 

69 

+  .33 

56 

—  .23 

70 

—  .15 

72 

—  .45 

—  .12 

21 

75 

4  -14 

59 

—  .08 

76 

—  .04 

67 

—  .02 

.00 

23 

39 

—  .09 

44 

4  .06 

42 

+  .60 

36 

—  .01 

4  .16 

For  Re  73  there  is  an  apparently  well  marked  correction  depending  on  a;  but  as 
it  is  not  supported  by  the  results  of  other  years,  I  have  thought  it  best  to  omit  the 
discussion. 

Wn  72. 

The  residuals  are  computed  from  the  standard  places  for  each  year.    In  the  dis- 
cussion, -  =  3  is  assumed. 
£/ 

Residuals  in  order  of  declinatioi 

DECLINATION  SUB  POLO. 


Wn70. 

Wn71-2. 

Wn73. 

Wn  74  * 

TUT           A 

*' 

r0 

Co 

n-' 

ro 

C0 

7t' 

ro 

Co 

*> 

ro 

Co 

6°8 

5 

-"10 

00 

9 

-'.'03 

'OO 

// 

// 

8 

-'.'25 

4  .% 

75 

14 

4  -57 

00 

12 

4  .00 

00 

7 

—  .30 

on 

19 

4  .36 

4  .38 

87 

21 

4  .07 

00 

35 

4  .24 

00 

27 

CO 

00 

34 

4  .76 

4  .21 

ABOVE  POLE. 

4  87 

27 

4    .12 

00 

36 

—    .39 

00 

29 

4     .20 

00 

33 

—    .24 

—  .21 

4  76 

16 

4    -14 

00 

8 

4    .34 

00 

4 

4     .20 

4     .02 

18 

—    .35 

—  .26 

4  70 

12 

—    .56 

00 

9 

—    .03 

00 

6 

—    .29 

4    .04 

14 

—    .19 

—  .33 

4  05 

22 

—    .09 

00 

23 

4    -15 

00 

10 

4    .31 

4     .07 

31 

—    .48 

—  .41 

4  56 

5 

4    .62 

00 

2 

4  1.19 

—  .04 

7 

—    .16 

4    -13 

10 

—    .72 

—  .55 

4  50 

25 

—    .45 

—  .06 

24 

—    .04 

'—  .10 

13 

4     .36 

4     .18 

24 

-     .45 

—  .62 

4  46 

15 

—    .45 

—  .08 

18 

4    .09 

—  .15 

16 

—    .15 

4     .23 

20 

—    .72 

—  .67 

4  39 

29 

4     .00 

—  .11 

32 

—    .25 

—  .23 

32 

4    -38 

4     .32 

44 

—    .76 

—  .74 

4  33 

9 

—    .18 

—  .13 

13 

—    .60 

—  .28 

13 

4    .15 

4     .41 

15 

—    .58 

—  .79 

4  27 

54 

—    .14 

—  .15 

69 

—    .  35 

—  .31 

51 

4     .49 

4     .49 

63 

—    .91 

—  .82 

4  21 

56 

.00 

—  .16 

71 

—    .27 

—  .34 

56 

4    .56 

4     .63 

72 

—    .  85 

—  .84 

4  14 

41 

—    .36 

—  .16 

76 

—    .53 

—  .33 

58 

4    .CO 

4     .56 

73 

—    .69 

—  .81 

4    9 

67 

—    .27 

—  .16 

9 

—    .26 

—  .32 

63 

4     .48 

4     .57 

95 

—    .64 

—  .76 

4    4 

ii9 

4    .19 

—  .14 

39 

—    .06 

—  .31 

33 

4     .81 

4     .59 

43 

—    .87 

—  .76 

—   1 

46 

4    .02 

—  .09 

56 

—    .29 

—  .30 

37 

4-    .51 

4    .63 

46 

—    .74 

—  .83 

—    8.5 

37 

4    .08 

—  .02 

60 

—    .49 

—  .28 

49 

4     .79 

4     -75 

50 

—  1.09 

—  .815 

—  14 

16 

4     .04 

00 

23 

—    .09 

—  .25 

16 

4     .86 

4     .84 

20 

—  1.18 

-  .78 

—  19 

6 

—    .59 

00 

11 

—    .43 

—  .23 

8 

4  1.57 

4     .92 

12 

—    .36 

—  .67 

—  22 

14 

4    .41 

00 

13 

—    .24 

—  .22 

12 

4  1.81 

4     .98 

16 

—    .78 

—  ,60 

—  28 

13 

—    .24 

00 

15 

—     .09 

-  .20 

11 

4      52 

4  l.l 

18 

—    .32 

—  .45 

—  34 

1 

—  1.3 

2 

4     -6 

2 

4  l.l 

*  See  explanation,  p.  157. 


[153] 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


559 


The  probable  error  is  derived  by  comparing  the  corrected  residuals  (collected  as 
cue  for  each  star)  with  the  standard  A5'. 
With  m  —  4:,  we  have: — 

E  =±".84. 

Taking  s  as  found  in  Section  V.,  and  e,  as  found  for  Wu  68  in  the  same  section,  we 
have: —  

E  =  ±  V(.70)2  +  (.25 f  =  ±  ".74. 

The  agreement  is  far  from  satisfactory.    The  former  result,  ±  ".84,  is  adopted. 
The  combined  results  of  all  the  years  are  next  arranged  in  order  of  right  ascen- 


sion. 


Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

Declination  limits. 

—  30°  to  +  5° 

+  5°to  +  40° 

+  40°  to  +  90° 

—  30"  to  +90° 

Mean  a 

7T7 

'•<>' 

IT 

'V 

7T7 

ra' 

tf 

r<> 

ft. 

// 

n 

II 

// 

1 

39 

+  .34 

162 

+  .16 

88 

+  .37 

289 

+  .25 

3 

15 

+  .08 

40 

—  .18 

35 

—  .07 

90 

—  .10 

5 

64 

-  .35 

109 

+  .23 

24 

+  .25 

197 

+  .04 

7 

33 

+  .15 

119 

+  .05 

42 

—  .36 

194 

—  .02 

9 

20 

—  .13 

88 

—  .14 

19 

—  .08 

127 

—  .13 

11 

58 

—  .16 

131 

—  .09 

36 

—  .57 

225 

—  .18 

13 

119 

—  .05 

53 

+  .23 

60 

+  .12 

2ii2 

+  .06 

15 

87 

+  .08 

121 

+  .16 

100 

+  .01 

308 

+  .09 

17 

33 

—  .05 

113 

—  .29 

80 

+  .03 

226 

—  .14 

19 

64 

+  .01 

148 

+  .01 

70 

—  .02 

282 

+  .00 

21 

68 

—  .44 

62 

—  .10 

111 

—  .14 

241 

—  .22 

23 

69 

+  .05 

51 

+  .39 

27 

—  .17 

147 

+  .13 

As  shown  under  Wn  68,  the  correction  in  order  of  A.  R.  found  for  the  declina- 
tions of  the  mural  circle  is  peculiar  to  that  instrument  or  observing-room  alone. 

The  following  tables  exhibit  the  results  deduced  for  systematic  correction  and 
weight  of  the  various  catalogues. 


560 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[154 


TABLE  IX. — Corrections  to  declinations. 
ORDER  OF  DECLINATION. 


& 

1 

£ 

o 

T-l 

00 
tS 

J3 

m 

1-4 

OJ 

bC 

w 

-M- 

8 

.a 
C5 

i 

p 

s 
£ 

gj 

o 
•< 

o 

C-3 

a 

O 

s 
w 

O 

d 

* 

,-H 

CO 

A 
02 

Si 

K 

O 
O 

•* 

CO 

m 
O 

// 

00 
00 
00 

—  .04 
—  .14 
—  .27 

—  .42 
—  .57 
—  .70 

—  .78 
—  .83 
—  .84 

—  .80 
—  .70 
—  .54 

—  .40 
—  .35 
—  .38 

—  .47 
—  .60 
—  .74 

—  .88 
—  .98 
—1.00 

—1.00 

TT 
CO 

& 
S 

£ 

M 

m 

6 

o 
+90 
+85 
+SO 

+75 
+70 
+65 

+60 

+55 
+50 

+45 
+40 
+35 

+30 
+25 

+20 

+15 
+10 
+  5 

±0 
-  5 
—10 

—15 
—20 
—25 

—30 
—35 
—40 

—50 
—60 
—70 

—80 
—90 

// 

// 

II 

II 

-.19 
—.22 
—.22 

—.23 
—.23 
—.22 

—.20 
—.18 
—.16 

—.15 
—.16 
—.17 

—.20 
—.21 
—.17 

—.05 
+.04 
00 

—.15 
—.24 
—.27 

—.25 
—.15 
00 

+.2 

o 
+90 
+85 
+80 

+75 
+70 
+65 

+60 

+55 
+50 

+45 
+40 
+35 

+30 
+25 

+20 

+15 

+10 
+05 

0 
—  5 
—10 

—15 
—20 
—25 

—30 
—35 
—40 

—50 
—60 
—70 

—80 
—90 

00 
00 
00 

00 
00 
00 

00 
—  .05 

—  .20 

—  .50 
—1.00 
—1.40 

—1.40 
—1.20 
—1.40 

—1.85 
—1.60 
—1.10 

—1.50 
—2.15 
—2.20 

—1.70 
—1.15 
—1.00 

—1.00 
—  1.00 
—1.  00 

00 
+.14 
+.29 

+.38 
+.30 
+.14 

—.02 
—.01 
+.12 

+.10 
.00 

00 
+.08 
+.06 

+.10 
+.13 
+.16 

+.18 
.+.16 
+.13 

+.09 

+.06 
+.06 

+.06 
+.07 
+.10 

+.13 

+.16 
+.19 

+.25 
+.33 
+.43 

+.55 
+.67 
+.78 

+.90 

"66 

00 

00 
00 
00 

00 
00 
00 

00 
00 
00 

00 
00 
00 

00 
—.05 
—.12 

—.17 
—.21 
—.24 

—.26 
—.27 
—.25 

—.22 
—.19 
—.15 

—.13 
—.12 
—.15 

—.21 

—.29 

—.38 

—.49 

—.60 
—.72 

—.84 
—.96 

00 
00 
00 

00 
00 
00 

00 
00 
—.02 

—.07 
—.13 
—.16 

—.22 
—.20 
—.29 

—.32 
—.36 
—.43 

—.52 

—.60 
—.68 

—.70 
—.70 

+  .10 
+  .12 
+  .15 

+  .15 
+  .13 
+  .08 

00 
—  .12 
—  .31 

—  .54 
—  .76 
—  .95 

—1.12 
—1.24 
—1.30 

—1.31 
—1.31 
—1.33 

—1.37 
—1.49 
—1.68 

—1.97 
—2.  50 
—2.85 

—2.95 

+.40 
+.40 
+.40 

+.40 
+.38 
+.31 

+.24 
+.17 
+.07 

—.03 
—.16 
—.20 

—.17 
—.14 
—.10 

—.07 
—.03 
00 

—.28 
—.38 
—.40 

—.52 
—.60 
-.62 

—.60 
—.54 
—.38 

—.14 

+.17 
+.32 

+.47 
+.50 
+.50 

+.41 
+.30 
+.14 

—.03 
-.20 
—.40 

+."35 
+.35 

+.35 
+.35 
+.35 

+.35 
+.35 
+.35 

+.32 
+.17 
00 

00 
00 
00 

00 
00 

[+1.30] 

+1.30 
+1.30 
+1.30 

+1.30 
+1.30 
+1.30 

+1.30 
+1.30 
+1.30 

+1.30 
+1.28 
+1.23 

+1.17 
+1.09 
+  .96 

+  .84 
+  .70 
+  .62 

+  .60 
+  .60 
+  .60 

+  .60 
+  .50 
+  .40 

+  .30 
+  .20 

—2."  66 

—1.10 
—  .34 

+  .20 

+  .52 
+  .57 
+  .43 

+  .14 
—  .06 
—  .14 

—  .14 
—  .04 
+  .16 

+  .46 
+  .71 

+  .88 

+  .90 
+  .71 
+  .47 

+  .10 

i  .00 

—  .08 

—  .10 
.00 















*  This  correction  is  subsequently  revised  with  the  definitive  AJ  and  Ap'. 

t  Dollen's  reduction. 

t  A  small  minus  correction  deduced. 

||  This  correction  is  considered  as  applicable  to  Dt  30,  after  "  com cliones  ultima"  (p.  357,  Struve's 
Pos.  Med.)  have  been  added. 

'•  The  correction  for  S  H  31  is  applicable  directly  to  the  catalogue  results  as  reduced  with  Young's 
refractions. 

ttFor  the  years  1833  and  1834  corrections  must  be  applied  for  defective  reading  of  barometer  (see 
Cambridge  Observations,  1835).  To  get  actual  corrections  to  catalogue  results  for  those  years,  the  effect 
of  this  correction  must  be  added  to  the  above. 


[165| 


REPORT  OP  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


561 


TABLE  IX.—  Corrections  to  declinations — Continued. 
ORDER  OF  DECLINATION. 


<? 

ri 

t£ 

MJ 

gj 

A 
0 

«_ 

i—" 

H 

-*- 
CO 

in 

U! 

$ 

& 

Wn  474 

% 
a 
0 

pj 

m 
ja 

e 

.—  < 

LI 

o 

02 

8 
£ 

f 

« 
U 

^ 

M 

M 

s 

£ 
C5 

(2 

0 

+90 

+85 
+80 

+75 
+70 
+  65 

+60 
+55 
+50 

+45 

+40 

+35 
+30 

+25 
+20 

+15 

+10 
+  5 

±  0 
—  5 
—10 

—  15 
—20 
—25 

—30 
—35 
—40 

—50 
—60 
—70 

—80 
—90 

II 

00 
—  .10 
-  .20 

—  .27 
—  .33 
—  .36 

—  .15 

+  .10 

+  .23 

+  .30 
+  .22 
+  .H 

+  .08 
+  .09 
+  .15 

+  .25 
+  .41 
+  .56 

+  .73 
+  .92 
+1.  13 

+1.34 
+1.55 
+1.77 

+2.00 

II 

00 
+  .01 
+  .03 

+  .05 
+  .08 
+  .09 

+  .10 
+  .11 
+  .12 

+  .12 
+  .13 
+  .14 

+  .15 
+  .17 
+  .19 

+  .23 
+  .28 
+  .34 

+  .41 

+  .49 
+  .59 

+  .70 
+  .83 
+  .97 

+1.10 

II 

00 
00 
00 

00 
—  .07 

—.18 

4;! 

—  .54 

—.65 
—.75 
—.83 

—.88 
—.90 
—.80 

—.60 
—.46 
—.50 

—.62 
—.70 
—.70 

—.68 
—.55 
—.4 

—.3 

II 

00 
+  .10 
+  .20 

+  .20 
+  .20 
+  .20 

II 

ft 
00 
00 
00 

00 
00 
—.02 

If 

00 
00 
00 

+.02 
+.04 
+.06 

+.08 
+.06 
+.00 

—.04 

—.02 
+.  05 

+.12 
+.15 
+.14 

+.10 
+.05 
+.  05 

+.08 
+.12 
+.15 

+.18 
+.22 
+.26 

+.30 

// 

00 
00 
00 

00 
+  .06 
+  .12 

+   .18 
+  .23 
+  .-6 

+  .30 
+  .33 
+  .35 

+  .37 
+  .38 
+  .39 

+  .41 
+  .44 
+  .46 

+  .49 
+  .53 
+  .59 

+  .68 
+  .84 
[+1.1J 

a 

00 
+.08 
+.14 

+.21 

+.26 
+.28 

+.29 
+.27 
+.22 

+.18 
+.12 
+.07 

+.01 
—.06 
—.12 

—.18 
—.26 
—.33 

—.37 
—.36 
—.30 

—.19 
—.02 

+.27 

+.7 

o 
+90 
+85 
+80 

+75 
+70 
+65 

+60 
+55 
+50 

+45 
+40 
+35 

+30 
+25 
+20 

+15 
+10 
+  5 

+  o 

—  5 
—10 

—15 
—20 
—25 

—30 
—35 
—40 

—50 
—60 

—70 

—80 
—90 

00 
+.25 
+.50 

+.66 

+.60 
+.42 

+.28 
+.10 
—.07 

—.20 
—.34 

—.48 

—.56 
—.60 
—.59 

—.45 
—.20 
+.04 

+.26 
+.44 
+.51 

+.47 
+.33 
+.16 

00 

+.10 
+.14 
+.15 

+.14 
+.10 
+.06 

—.02 
—  .  05 
—.05 

—.05 
—.05 
—.05 

—.08 
—.14 
—.21 

—.29 
—.34 
-.35 

—.34 
—.31 
—.27 

—.23 
—.18 
—.11 

-.03 

00 
00 
00 

00 
00 
—.10 

—.26 
—.42 
—.57 

-.69 

—.81 
—.87 

—.84 
—.65 
—.33 

—.10 
—.05 
—.05 

—.07 
—.11 
—.13 

—.12 

—.08 
—.04 

00 

—.12 
—.13 
—.13 

—.14 
—.15 
—.16 

—.18 
—.20 
—.21 

—.20 
—.16 

—.08 

+.02 
+.10 
+.17 

+.18 
+.16 
+.11 

+.04 
00 
00 

+.  Of) 
+.13 
+.20 

+.24 





+  .16 
00 
—  .35 

—  .75 
—  .81 
—  .63 

—  .42 
—  .25 
—  .S7 

—  .47 
—  .74 
—1.04 

—  1.  20 
—1.24 
—1.11 

—  .87 
—  .48 

+."30 
+.29 

+.27 
+.26 
+.24 

+.23 
+.21 
+.20 

•hi' 

+.16 
+.13 

+.10 

+.06 
00 

—.05 

-.08 
—.08 

—.06 
—.03 
00 

+.05 
+.12 
+.19 

+.27 
+.34 
+.36 

+.34 
+.  25 
+.13 

+.02 
—.08 
—.15 

—.21 

+  .40 
+  .53 

+  .68 
+  .80 
+  .90 

+  .99 
+1.04 

+1.08 

+1.11 
+1.13 
+1.12 

+1.09 
+1.06 
+1.  02 

+  .99 
+  .95 

+  .92 

+  .85 

+  .63 

+  .38 

+  .19 

±    00 

*  To  the  declinations  of  years  1836  and  1837  —  ".09  was  added  before  deriving  tbe  above. 

t  Applicable  to  declinations  as  reduced  in  this  paper  (pp.  27  to  32). 

I  To  declinations  of  Wn  1845,  — ".25  was  first  added  for  error  of  assumed  latitude,  before  deriving 
tbu  above  table. 

||  The  correction  —  ".43  was  first  applied  to  all  declinations  on  the  authority  of  latitude  discussion 
made  in  this  paper  (p.  26).    The  true  correction  to  catalogue-places  is  therefore  —  ".43  +  values  taken 
from  the  above  table  for  Ce  48.  • 
-36 


562 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


|15fiJ 


TABLE  IX. — Corrections  to  declinations — Continued 
ORDER  OF  DECLINATION. 


3D 

O 

t 

£ 

§ 

% 

$ 

g 

53 

ri 

d 

§ 

3 

s 

* 

a 

W 

o 

3 

(? 

o 
to 

1 

& 

« 

o 

U 

3 

u 

& 

& 

& 

a 

1 

£ 

+90 

—.15 

—.35 

+.22 

—  .20 

00 

+.30 

—.20 

+.20 

+.08 

00 

4-90 

+85 

—  .05 

—.30 

+.26 

—  .23 

+.02 

+.44 

—.19 

+.26 

+.11 

00 

-4-85 

+80 

+.05 

—.25 

+.30 

—  .26 

+.05 

+.56 

—  .  Hi 

+.32 

+.  12 

00 

+80 

+75 

+.12 

—.20 

+.31 

—  .31 

+.09 

+.  66 

—.10 

+.38 

+.11 

00 

+75 

+70 

..... 

+.17 

—.15 

+.31 

—  .36 

+.  15 

.--.-.  - 

+.73 

—.04 

+.40 

...... 

+.08 

00 

+70 

+65 

+.18 

—.12 

+.30 

—  .44 

+.21 

+.70 

+.01 

+.39 

+.05 

00 

+65 

+60 

+.16 

—.10 

+.22 

—  .55 

+.23 

+.60 

+.04 

+.26 

+  02 

00 

+60 

+55 

+.13 

—.09 

+.07 

—  .77 

+.21 

+.46 

+.07 

+.06 

—  02 

00 

-t-55 

+50 

+.10 

—.11 

—.13 

—1.12 

+.15 

f—  2.41 

+.20 

+.10 

—  .17 

—  05 

00 

+50 

+45 

+.05 

—.15 

—.36 

—1.40 

+.11 

r—  LSI 

—.12 

+.10 

—.29 

—  09 

00 

4-45 

+40 

+.50 

00 

—.20 

—.52 

—1.45 

+.11 

—  .80 

—.42 

+.OD 

—.32 

+.50 

—.13 

00 

+40 

+35 

+.  50 

—.04 

—.24 

—.52 

—1.41 

+.15 

—  .30 

—.65 

+.04 

—.27 

+.46 

—.18 

+.  05 

+35 

+30 

+.49 

—.09 

—.28 

—.46 

—1.29 

+.24 

—  .06 

—.80 

00 

—.11 

+.42 

—.25 

+.10 

+30 

+25 

+.48 

—.13 

—.33 

—.37 

—1.  13 

+.:« 

—  .05 

—.74 

—.06 

+.04 

+.39 

—.33 

+.13 

H25 

+20 

+.44 

—.18 

—.35 

—.47 

—  .87 

+.37 

—  .10 

—.56 

—.12 

+.03 

+.38 

—.40 

+.15 

+20 

+15 

+.31 

—.23 

—.36 

—.62 

—  .67 

+.38 

—  .  15 

—  .  35 

—.15 

—.08 

+.38 

—  .  45 

+.12 

+15 

+10 

+.20 

—.26 

—.36 

—.70 

—  .58 

+.35 

—  .18 

—.09 

—.19 

—.10 

+.52 

—.46 

+.07 

+  10 

+05 

+.15 

—.27 

—.35 

—.75 

—  .57 

+.28 

—  .20 

+.20 

—.20 

-.06 

+.71 

—.44 

—.02 

+05 

0 

+.27 

—.26 

—.34 

—.68 

—  .55 

+.20 

—  .23 

+.51 

—.18 

—.0:1 

+.87 

—.40 

—.09 

0 

—  5 

+.40 

—.23 

—.30 

—.45 

—  .53 

+.15 

—  .26 

+.70 

—.13 

00 

+.90 

—.35 

—.10 

—  5 

—10 

+.39 

—.17 

—.20 

—.23 

—  .49 

+.21 

—  .26 

+.79 

—.04 

00 

+.86 

—.28 

—.00 

—10 

—15 

+.12 

—.10 

—.05 

—.20 

—  .46 

+.26 

—  .20 

+.79 

+.10 

00 

+.75 

—.10 

+.14 

—15 

—20 

—.07 

—.02 

+.14 

—.23 

—  .42 

+.26 

—  .  15 

+  .68 

+.  2h 

00 

+.63 

—.10 

+.27 

—20 

—25 

—.14 

+.06 

+.35 

—.27 

—  .39 

+.25 

—  .10 

+.40 

+.50 

00 

+.50 

00 

+.40 

—25 

—30 

—.02 

+.16 

+.60 

—.30 

[-.35] 

[+.20] 

—  .or> 

[+•10] 

+.70 

00 

+.44 

+.10 

[+.55] 

—30 

—35 

4-.  13 

00 

_1_    01 

35 

—40 

+.27 











+  .05 







+.08 





—40 

—50 

+  «7 

+  .  15 

.14 

—50 

—60 

+.11 

-4-    27 

20 

60 

—70 

00 

+    26 

20 

70 

—80 

00 

+     13 

08 

80 

—90 

00 

00 

00 

—90 

*  The  correction  for  error  of  n-sumed  latitude,  flexure,  division,  &c.,  given  in  the  introduction  to 
the  Williamstown  catalogue,  must  also  be  applied.  The  true  correction  is,  therefore :  Correct  on  taken 
from  introduction  Me  62  +  correction  of  above  table. 

tTo  the  catalogue  declinations  from  direct  observations  above  pole  for  1861  and  1862  \vaslirst 
added  the  correction —".  68  (+ ".68,  below  pole);  and  to  the  declinations  of  years  186:?-18(>5  =p".47, 
according  as  the  declination  results  from  observations  above  or  below  the  polo.  The  actual  correction  is, 
therefore:  These  qunntities+  corrections  from  above  table. 


[157] 


KEPOKT  OF  THE  OUIEF  ASTKONOMEE,  APPENDIX  H. 


563 


TABLE  IX. — Corrections  to  declinations — Continued. 
OEDEE  OP  DECLINATION. 


6 

«J 
CD 

& 

g 

CO 

m 

s 
£ 

CO 

to 

« 

6 

J 

ts 

a 
i? 

g 

1 

g 
1 

o 

F 

a 
O 

-»- 
o 
l~ 

a 
£ 

i 

1—  1 

r* 

1 

Wn73. 

+f 

•<* 
t- 

c 

* 

& 

o 
+90 
+85 
+80 

+75 
+70 
+65 

+60 
+55 
+50 

+45 
+40 
+35 

+30 

+25 
+20 

+15 

+10 
+05 

0 

—  5 
—10 

—15 
—20 
—25 

'10 

it 
20 

ii 

+.20 
+.26 
+.32 

+.38 
+.40 
+.39 

+.26 
+.06 
—.17 

—.29 
—.32 
—.27 

—.11 

+.04 
+.03 

—.08 
—.10 
—.06 

—.03 
00 
00 

00 
00 
00 

00 

II 

—.20 
—.20 
—.20 

—.20 
—.17 
—.11 

-.01 
00 
—.01 

—.07 
—.15 
—.18 

—.14 
—.06 
—.06 

—.15 
—.24 
—.27 

—.28 
—.24 
—.17 

—.07 
+.07 
+.25 

+.48 
+.75 

II 

+.40 
+.41 
+.55 

+.71 

+.71 
+.54 

+.05 
—.36 
—.56 

—.60 
—.57 
—.50 

—.38 

—.28 
—.24 

—.20 
—.20 
—.25 

—.33 

—.40 
—.40 

—.40 
—.40 
—.40 

[-.40] 

li 

4-  .22 
+  .47 
+  .72 

+  .94 

+1.00 
+  .90 

+  .70 
+  .44 
+  .18 

—  .04 
—  .23 
—  .37 

—  .47 
—  .54 
—  .55 

—  .52 
—  .47 
—  .43 

—  .43 
—  .43 
—  .43 

-  .39 
—  .30 

—  .18 

—  .05 

II 

00 
00 
00 

—.01 
—.05 
—.10 

—.17 

—.22 
—.25 

—.26 
—.2o 
—.26 

—.26 
—.26 
—.26 

—.25 
—.23 
—.19 

—.12 

—.05 
+.03 

+.11 

a 

a 

00 
+  .02 
+  .05 

+  .10 
+  .15 
+  .20 

+  .26 
+  .32 
+  .36 

+  .39 
+  .42 
+  .45 

+  .47 
+  .50 
+  .53 

+  .55 

+  .57 
+  .58 

+  .59 
+  .59 
+  .60 

+  .63 

+  .70 
+  .80 

+  .93 
+1.09 

a 

00 
—  .09 
—  .15 

—  .20 
—  .25 
—  .30 

—  .34 
—  .37 

—  .40 

—  .41 
—  .42 
—  .42 

—  .37 
—  .33 
—  .33 

—  .40 
—  .52 
—  .65 

—  .80 
—1.00 
—1.20 

—1.43 
—1.66 
—1.93 

r    °  °oi 

o 
+90 
+85 
+80 

+75 
+70 
-t-65 

+60 

+55 
+50 

+45 
+40 
+35 

+30 
+25 
+20 

+15 

+10 

+05 

0 
—  5 
—10 

—15 
—20 
—25 

—30 
—35 
—40 

—50 
—60 
—70 

—SO 
—90 

.00 
.00 
.00 

.00 
.00 
.00 

.00 
—  .03 
—  .06 

-  .09 
—  .11 
—  .13 

—  .14 

—  .15 
—  .16 

—  .16 
—  .16 
—  .15 

—  .10 
—  .05 
.00 

00 
00 
00 

00 
00 

00 
00 
00 

00 
00 
00 

00 
—.05 
—.10 

—.16 
—.22 
—.26 

—.30 
—.33 
—.34 

—.33 
—.32 
—.31 

—.30 
—.29 
—.27 

—.25 
—.23 
—.21 

19 

00 
00 
00 

+  .02 
+  .04 
+  .07 

+  .10 
+  .14 

+  .18 

+  .24 
+  .30 
+  .38 

+  .46 
+  .51 
+  .54 

+  .56 
+  .57 
+  .58 

+  .61 

+  .69 
+  .77 

+  .86 
+  .94 
+1.03 

+1.11 

+.07 
—.04 
—.14 

—.24 
—.33 
—.41 

—.49 
—.56 
—.62 

—.68 
—.73 

—.77 

—.81 
—.83 

—.84 

—.82 
—.76 
—.75 

—.82 
—.85 
—.86 

—.76 
—.65 
—.53 

40 

2'j 

—  .25 

—  .26 
—  .27 
—  .27 

—  .25 
—  .21 
—  .22 

—  .  26 
—  .30 
—  .30 

—  .22 
—  .10 
—  .05 

—  .06 
—  .15 
—  .22 

—  .23 
—  .19 
-  .10 

+  .07 
+  .35 
+  .66 

+1.00 
+1.35 



i+i~25] 

[+1.00] 
[+  -67] 
+  .48 

+  .11 

—  .08 
—  .15 

—  .15 
—  .15 
—  .15 

—  .16 
—  .18 
—  .21 

—  .26 
—  .30 
—  .32 

—  .36 
—  .38 
—  .40 

—35 
—40 

—50 
—60 
—70 

—80 
—90 



—.17 

—.29 

—  .34 

—  .22 

—  .12 

—  .05 

00 

'Applicable  to  declinations  derived  in  this  paper  (Section  V.). 

t  Applicable  to  declinations  of  annual  catalogues  after  correction,  as  explained  in  Section  V. 

tAs  explained  elsewhere  the  correction,  +".82,  to  the  declinations  of  1874,  south  of  Wn.  zenith 
was  neglected  by  accident  for  stars  south  of  — 12°  declination,  and  the  error  discovered  too  late  to  be 
corrected  in  the  succeeding  results.  As  actually  used  in  making  up  the  definitive  C,,  of  the  final  dis- 


564 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[158J 


TABLE  IX. — Corrections  to  declinations — Continued. 
EADCLIFFE  ANNUAL  CATALOGUES. 


6 

62.* 

63. 

64. 

65. 

66. 

67. 

68. 

69. 

70. 

71. 

72. 

73. 

<5 

0 

it 

II 

„ 

II 

a 

„ 

II 

II 

„ 

// 

II 

It 

o 

+00 

00 

00 

+.40 

+  .10 

+  -74 

00 

+  .10 

00 

+  .10 

+.23 

+.17 

.00 

+90 

+1-5 

—  .26 

—  .17 

+.2C 

+  .2? 

+1.00 

00 

+  .15 

00 

+  .13 

+.27 

+.94 

+.21 

+85 

+80 

—  .48 

—  .34 

+.13 

+  .38 

+1.26 

00 

+  .18 

00 

+  .17 

+.31 

+.3y 

+.39 

+80 

+75 

—  .66 

—  .50 

00 

+  .41 

+1.43 

00 

+  .19 

—.03 

+  .19 

+.36 

+  .40 

+.52 

+75 

+70 

—  .86 

—  .63 

—.13 

+  .40 

+1.50 

00 

+  .20 

—.06 

+  .20 

+.40 

+.48 

+.07 

+70 

+65 

—1.03 

—  .73 

—.26 

+  .31 

+1.41 

00 

+  .18 

—.12 

+  .19 

+.42 

+.50 

+.80 

+65 

+60 

—1.21 

—  .81 

—.40 

+  .20 

+1.21 

00 

+  .13 

—.23 

+  -17 

+.44 

+.51 

+.86 

+60 

+55 

—1.36 

—  .87 

—.55 

+  .08 

+  .96 

—  .10 

+  .08 

—.30 

+  .12 

+.41 

+.49 

+.82 

+55 

+50 

—1.49 

—  .90 

—.70 

—  .03 

+  .60 

—  .22 

00 

—.34 

+  .11 

+.35 

+.42 

+.70 

+50 

+45 

—1.56 

—  .90 

—.75 

—  .10 

+  .47 

—  .37 

—  .06 

—.32 

—  .01 

+.23 

+.33 

+.47 

+45 

+40 

—1.60 

—  .90 

—.80 

—  .14 

+  .20 

—  .46 

—  .10 

—.27 

—  .22 

+.  1C    +.15 

+.21 

+40 

+35 

—1.60 

—  .85 

—.74 

—  .18 

—  .02 

—  .48 

—  .09 

—.28 

-  .50 

—.10 

—.07 

—.02 

+35 

+30 

—1.52 

—  .85 

—.62 

—  .18 

—  .14 

—  .47 

+  .03 

—.28 

—  .63 

—.27 

—.21 

—.13 

+30 

+25 

—1.51 

—1.00 

—.55 

—  .18 

—  .30 

—  .49 

+  .12 

—.33 

—  .65 

—.25 

—  .  17 

—.06 

+25 

+20 

—1.60 

—1.20 

—.50 

—  .21 

—  .51 

—  .58 

+  .07 

—.48 

—  .40 

—.10 

+.08 

+.10 

+20 

+15 

—1.68 

—1.23 

—.50 

—  .33 

—  .88 

—  .73 

—  .06 

—.62 

00 

+.20 

+.  32 

+.21 

+15 

+10 

—1.67 

—1.20 

—.42 

—  .42 

—1.06 

—  .88 

—  .10 

—.66 

+  .26 

+.40 

+.44 

+.23 

+10 

+  5 

—1.  54 

—  .87 

—.20 

—  .26 

—  1.  11 

—1.00 

—  .10 

—.56 

+  .20 

+.36 

+.40 

+.11 

+  5 

0 

—1.14 

—  .38 

+.25 

+  .13 

—  .93 

—  .88 

-  .10 

—.47 

00 

+.18 

+.30 

-.09 

0 

—  5 

—  .78 

+  .10 

+.48 

+  .40 

—  .91 

—  .74 

—  .20 

—.40 

—  .25 

+.02 

+.18 

—.26 

—  5 

—10 

—  .59 

+  .02 

+.56 

+  .53 

—1.06 

—  .79 

—  .35 

—.40 

—  .50 

—  .11 

+.07 

—.34 

—10 

—15 

—  .43 

+  .09 

+.56 

+  .62 

—1.30 

—  .89 

—  .51 

—.40 

—  .65 

—.24 

-.02 

—.35 

—15 

—20 

—  .30 

+  .13 

+.58 

+  .80 

—1.57 

—1.05 

—  .67 

—.40 

—  .80 

—.34 

—.11 

—.30 

—20 

—25 

—  .20 

+  .16 

+.65 

+  .90 

—1.83 

—1.22 

—  .83 

—.35 

-  .90 

—.42 

—.20 

—.25 

—25 

—30 

—  .10 

+  .18 

+.72 

+1.00 

—2.10 

—1.40 

—1.00 

—.30 

—1.00 

—.50 

—.28 

—.20 

—30 

cussion  of  declinations,  Wn  74  was  used  as  above  from  +  90°  to  + 15°.     From  that  point  the  corrections 
were  virtually  computed  according  to  this  table : 


(5 

Corr. 

6 

Corr. 

o 

// 

o 

// 

+  10 

—  .78 

—  15 

—  .99 

+     5 

—  .72 

—  20 

—  .77 

00 

-  .65 

—  25 

—  .55 

—  05 

—  .55 

—  30 

—  .34 

—  10 

—  .38 

—  35 

—  .13 

That  is,  as  actually  used,  a  declination  of  Wn  74  (+  10°  to  —  35C),  a«  given  in  the  catalogue,  was 
corrected  by  +  ".82  -f-  the  values  given  in  this  table. 

•As  explained  under  Re  66,  the  corrections  from  +  35°  to  +  90°,  for  (he  annual  catalogues  He  62- 
Kc  66  are  deserving  of  little  confidence. 


159] 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


565 


TABLE  X. — Corrections  to  declinations. 
ORDER  OF  RIGHT  ASCENSION. 


S~ 

IS 

j 

. 

I 

a 
a 

II 

1 

O 
1—1 

f-H 

n 

| 

* 

o 

ti 

n 

o  ° 

1-t 

g 

§8 

i 

a 

£ 

gj 

cc 

w1 

® 
O 

M 

JS 

£ 

£ 

£ 

a 

h. 

a 

II 

II 

II 

n 

II 

II 

„ 

II 

„ 

„ 

if 

ft 

0 

—.18 

+.40 

+.47 

+.32 

—.  15 

+.13 

—.19 

—.12 

—.18 

—.05 

+.01 

—.15 

12 

1 

—.04 

+.25 

+.53 

+.38 

—.11 

+.08 

—.19 

—.17 

—.12 

00 

+.05 

—.07 

13 

2 

+.11 

+.08 

+.55 

+.40 

—.06 

+.03 

—.19 

—.21 

—.04 

+.  05 

+.09 

+.02 

14 

3 

+.25 

—.09 

+.53 

+.40 

—.00 

—.02 

—.17 

—.23 

+.04 

+.10 

+.12 

+.11 

15 

4 

+.37 

—.26 

+.47 

+.37 

+.06 

—.07 

—.14 

—.24 

+.12 

+.14 

+.15 

+.19 

16 

5 

+.46 

—.41 

+.39 

+.32 

+.11 

—.12 

—.09 

—.24 

+.19 

+.17 

+.16 

+.26 

17 

6 

+.53 

—.53 

+.27 

+.24 

+.15 

—.16 

—.05 

—.21 

+.24 

+.20 

+.17 

+.31 

18 

7 

+.56 

—.62 

+.14 

+.15 

+.18 

—.19 

00 

—.18 

+.28 

+.20 

+.16 

+.34 

19 

8 

+.55 

-.66 

00 

+.05 

+.20 

—.20 

+.05 

—.13 

+.30 

+.19 

+.14 

+.34 

20 

9 

+.50 

—.66 

—.14 

-.06 

+.21 

—.20 

+.10 

—.07 

+.30 

+.17 

+.12 

+.33 

21 

10 

+.42 

—.62 

—.27 

—.16 

+.20 

—.19 

+.14 

—.00 

+.28 

+.14 

+.08 

+.29 

22 

11 

+.31 

—.53 

—.39 

—.25 

+.18 

—.16 

+.17 

+.06 

+.24 

+.10 

+.04 

+.23 

23 

12 

+.18 

—.40 

—.47 

—.32 

+.15 

—.13 

+.19 

+.12 

+.18 

+.05 

—.01 

+.15 

24 

NOTE. — When  a  is  taken  from  right-hand  (12A  to  24A)  the  signs  of  the  table  are  reversed. 
*  The  corrections  for  Ce  40  and  Bn  66  are  applicable  only  within  the  declination  limits  —  30°  to +  40°. 

In  computing  from  tbe  values  of  J7,  given  in  the  preceding  pages,  the  definitive 
weights  to  be  used  in  the  final  discussion,  ±  ".30  was  taken  as  the  probable  error  of  tho 
unit,  and  5  (corresponding  to  a  probable  error  of  ±  ".134)  as  the  maximum  weight. 
Weight  .05  is  used  in  a  few  cases.  As  the  probable  errors  are  somewhat  uncertain, 
especially  in  their  respective  relation  to  number  of  observations,  only  the  denomina- 
tions of  weight  presented  in  the  table  were  actually  used. 

For  convenience,  a  few  weights  deduced  in  Section  IX.  are  also  collated  here. 

With  the  "Catalogue"  as  an  argument,  the  corresponding  horizontal  line  is  fol- 
lowed until  the  number  of  observations  is  reached,  or,  at  least,  the  limits  which  include 
it.  At  the  top  of  the  column  is  found  the  corresponding  weight. 

The  second  argument  is,  however,  often  a  probable  error  (as  Kg  21,  Dt  24,  etc.),  or 
weight  resulting  from  the  system  of  compilation  (as  with  Ce  40,  Eh  43,  etc.). 


566  UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.         [160J 


TABLE  XL —  Weights  used  in  discussion 


Catalogue. 

Weights. 

.05 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

Number  of  observations,  preliui 

GIi  1732 

2  to  8  . 

2  or  3 

4  to  20  . 

All 

Ior2  
errors  

3  to  5  

6tol8.... 

19  or  more. 

Kg  21  

Probable 

.44  to  .41.. 

.40  to  .37.. 

.36  or  35... 

.34  or  .33.. 

Bt  24  and  30. 

Same  as 

Kg   21   or 

Ao  29,  acco 

rding  as  pro 

bable  error 
All  

or  number 

of  observati 

ons  is  the 

argument  .  . 

1  

2 

All 

C  G  H  31 

land  2.... 
8  or  3  

3  to9  
»to9  

10  or  more. 
10  to  21... 

S.  11.31  

1  

22  to  85... 

85  or  more. 

1 

2... 

3  

4  

5  and  6 

7 

M  h  '14 

1  and  2... 

3 

4to6  

7  loll  .... 

12  to  18... 

19  to  35  ... 

36  or  more  . 

ils35  
Eh  37 



2  or  3  

4  or  more 

1  

2... 

3  

4         

All 

Gh  39 

I 

3  

3  

4  

5  

6 

Weights 

1  

2  

3 

Eh  43 

Weights 

1 

S... 

3 

4 

Gh  45 

1 

2  

3  

4 

Pa  45 

Sec  table 

Ue  45 

1... 

2or3  
5tol4  

4and5.... 

6  to  10  .... 

11  to  23  ... 

24  or  more. 



Ah  4  land  52. 
Wn  47 

1 

2  to  4  .... 
1. 

Weights  . 
Same  as 

2  

3  

4  

5 

O  48 

Ce40 

Wn48(P.T.) 
Ms  50 

1 

2  

3 

4 

3to5  .   ... 

Gh  51 

Same  as 

Gh39   

So  51 

1  

2 

3  to  5  ... 

6  to  11  .... 

12  to  37  .. 
2  

38  or  more. 

Pa  53    

1  

3  

So  55 

1...  . 

2  and  3  

2 

4to7  
3  

8tol9.... 
4  

20  or  more. 

WD  56 

1  

7  

8  and  9.  .  . 
2... 

10  to  12  ... 

Ps  56    . 

1  

Bs  56 

1 

2 

Sand  4.... 

5to7  

8and9.... 

10  to  16... 

17  to  27  ... 

28  to  52  ... 

Co  56 

Same  as 

Ce  40  

Gh  57   

1  

2 

C.G.  H.  58... 

1  

2  

3 

Re  58 

Same  as 

Re  45  

Eh  58    . 

1        

2  

3  

4  or  5 

6to8  

9  to  15.... 

16  or  more  . 
1 

psGO    

BsCO  

1... 

2  

3  

4 

Me  02 

1. 

2  and  3  

4to6  

7tol7  .... 

18  or  more. 



Pa62(P.V.). 
Eh  63  
Wn64  
Gh64 

Same  as 
Weights 
Same  as 

Eh  58    ... 

1  

8  

3  

4  

Gh57 

Ps64  

1 

Bs65  

1  

8 

P860  

Same  as 

Ps  64 

BnC6  ... 

Lc67  

Ln  67  

Eh  67  

2  to  5 

Me  68... 

1  

2... 

Wn  68  
Ee  66  and  72. 
Gh70  

Weights  . 

1... 

2 

3 

4  and  5 

6 

7 

S 

9 

1  

2or3  

4or5  
1 

6to9  

10  to  14  ... 
2 

15  to  23  ... 

24  to  44  ... 
3 

45  to  152  .. 
4 

Wn70  

Ior2  

3  to  5 

Wn72  

Weights  . 

2  . 

3  

4 

5 

6 

[161] 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


567 


of  definitive  decimations. 


Weights. 

Catalogue. 

1.0 

1.5 

3.0 

2.5 

3.0 

3.5 

4.0 

5.0 

imiry  weight,  or  probable  error. 

Gh  1752. 
Gh  1755. 
Po  1600. 
Bh  1810. 

KR  21. 
Gh22. 
Dt24and30. 
Va29. 
Ao29. 
Gh30. 
C.  G.  H.  31. 
S.  II.  31. 
C.  G.  H.  33. 
Ce34. 
Mh34. 
Ms  35. 

Eh  37. 
Kg  38. 
Gh39. 
Co  40. 
Kg  43. 
Eh  43. 
Gh45. 
Pa  45. 
Ee  45. 
All  -tUndra. 
Wn47. 
Ce48. 
Wn48(P.V.) 
Ma  50. 

Gh  51. 
So  51. 
PS  53. 
So  55. 
Wn  S6. 
Ps  56. 
Bs56. 
Co  56. 
Gh57. 
C.  G.  H.  58. 
Ee58. 
Eh  58. 

Ps  60. 
Bs60. 
Me  62. 
Pa62(P.T.) 
Eh  63. 
Wn64. 
(J'u  ci. 
PsC4. 
Bs65. 
PsC6. 
Bn66. 
Lc  fi7. 
Lu07. 

Eh  67. 

Mo  68. 
Wn68. 
Ke  66  and  73. 
Gh  70. 
Wn70. 
Wn73. 

.32  to  .37  ... 
All 

.26  to  .33.. 

.22  to  .20.... 

.19  

.18  and  .17  .. 

.16  

.15  

.14  or  less  .  .  . 

3 

4to6  

7  to  10 

11  to  16... 

17  to  29  

30to68  

All 

8  to  18 

5  to  12 

13  or  more. 

7  to  11 

12  to  21  .  . 
5to8  
All 

22  to  45  
9  to  13  

46  to  156.. 
14  to  19... 

4 

20  to  28  ..T.. 

29to38  

39  to  55  

56  or  more  .  . 

5  and  6  

7  and  8... 
9  to  14  .... 

9  to  11  .. 
15  to  26  

13  and  13.. 
27  to  50... 

14  to  16  ... 
51  to  139 

17  and  18  

19  to22  

33  or  more  .  . 

5  to  8 

6  and  7 

8  to  10  

11  to  13  

i4to"l6... 

17  to  19  

20  "to"  22  

23  to  27  

38  or  more  .  . 

4  to  7 

8  to  15  .... 

16  to  39  

40  or  more. 

13  to  27  
3to5  

23  to  124  .. 
6tol8  .... 

125  and  more 

3  and  4 

5to7  
10  or  more. 

8  to  12 

13  to  21  ... 

22  to  44  

45  to  207  .... 

208  or  more  . 



4  to  9    

2  

5  to8 

3... 
9to  18  .... 

4toG  
19  to  no  

7tol2.... 
61  or  more. 

13  to  30  

1 

2  

3  or  more  .  .  . 

5  and  6  

7to9  

10  to  12  

13  to  15  ... 

16tol8  .... 

19  and  20  

2 

3to5  
4  aiid  5  — 

(i  to  13  ... 
C  to  8 

13  to  52  ... 
9tol3  .... 

53  or  more  .  . 
14  to  21  

'm'd  37*  .'."".' 

38  and  more 



3 

All 

All 

All  not  fun- 
damental  or 
circnm  polar. 

Fundamental 
and  circum- 
polnr. 

3  to  6    .. 

7toS4.... 
14tol9... 

10  to  13  

20  to  25  

26  to  30  ... 

31  to  36  

37  to  41  

42  to  49  

50  or  more  .  - 

5to7    

8  to  17  .... 

18  to  47  

48  or  more. 

7  to9      . 

10  to  13  ... 

14  to  17  

18  to  21  ... 

22  to  25.... 

26  to  29  

30  to  35  

36  or  more  .  . 

568 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[162] 


NOTE  1.— The  Poulkova  observations  are  weighted  according  to  the  probable  errors  given  on  pp.  (29) 
and  (30)  of  introduction  (Vol.  V.).  The  weight  is  slightly  reduced  in  two  cases.  Following  is  the  table 
of  weights.  Between  +  55°  and  -f-  65°  declination,  when  the  observations  are  above  the  pole,  the 
weights  of  the  first  line  are  multiplied  by  .4  : 


6 

1  obs. 

2  obs. 

4  obs. 

8  obs. 

16  obs. 

+  40°  to  55°  and  65°  to  80°  ... 
-)-  30°  or  +  90°    

1 
1 

9 
9 

3 
3 

4 
4 

5 
6 

+  20°  or  -f  80°  S  P    

1 

2 

a 

4 

5 

+  10°  or  +  70°  SP  

.8 

1.5 

2.5 

3.5 

4 

+  00  or  +  60°  S  P   

.5 

1.0 

1.5 

2.5 

3.5 

10°  or  +  50°  S  P 

3 

.5 

1.0 

1.5 

2.5 

15°  or  +  45°  S.  P   

.2 

.3 

.7 

1.0 

2.0 

NOTE  2.— When  the  zenith  distance  of  a  star  observed  at  a  given  observatory  is  greater  than  7UU 
the  above  weights  are  multiplied  by  the  following  arbitrary  numbers: 


Z  D 

Factor. 

ZD 

Factor. 

o 

o 

70 

1.0 

76 

5 

71 

.9 

77 

4 

72 

.8 

78 

3 

73 

.7 

79 

3 

74 

.6 

80 

9 

75 

.5 

NOTE  3.— In  nsiug  the  later  Greenwich  catalogues  (Gh  57, 64,  and  70),  Ps  64  and  Ps  66,  and  Bs  60  and 
Bs  65,  a  considerable  modification  of  the  above  weights  takes  place,  whenever  the  same  star  is  observed 
in  two  or  more  series  at  each  observatory.  The  maximum  weight  given  to  Gh  57,  64,  and  70  combined, 
is  7.0 ;  to  Ps  64  and  Ps  66,  4.0 ;  and  to  Bs  60  and  Bs  65,  5.0.  Where  the  combined  weights  were  smaller 
than  these  totals,  arbitrary  reductions  of  each  are  made;  these  reductions  being  proportionally  less,  the 
fewer  the  observations.  This  course  is  taken  because,  strictly  speaking,  the  catalogues  of  the  respective 
groups  are  really  parts  of  the  same  series  and  have  to  some  extent  the  same  errors.  Of  course,  when 
either  of  the  above-mentioned  catalogues  stands  as  the  sole  representative  of  its  observatory  it  receives 
the  full  tabular  weight.  In  a  less  degree  this  reduction  of  weights  is  applicable  to  groups  of  catalogues 
not  included  in  the  above  enumeration ;  but  in  all  such  cases  it  is  believed  that  the  reduction  of  weights 
required  is  without  practical  consequence  to  the  final  result. 

With  the  values  of  C  computed  in  Section  V.,  and  with  the  corrections  and  weights 
of  Tables  IX.,  X.,  and  XI.,  the  definitive  values  of  J<S  and  J/  are  next  computed  for 
436  stars,  a  and  8  Ursse  Minoris  are  allowed  to  stand  as  first  computed,  and  62  others 
are  reserved  until  systematic  corrections  shall  have  been  derived  for  certain  authorities 
from  the  definitive  places. 

The  conditional  equations  are  so  constructed  as  to  give  J<S  for  1875.  Much  care 
has  been  exercised  in  these  computations,  and  the  usual  checks  have  been  faithfully 
employed. 

Column  €„  in  "  Details  of  Corrections  to  Assumed  Declinations"  is  computed  from 
C,  by  the  addition  of  corrections  taken  from  Tables  IX.  and  X.  Column  n  is  next 
formed  from  Table  XL,  subject  to  the  limitations  expressed  in  notes  2  and  3  above. 
The  epochs  are  taken  from  column  "Cat."  The  resulting  values  of  J<'  and  J//.'  fire 


[103] 


REPORT  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


569 


given  iu  the  catalogue  at  the  end  of  this  paper.    With  these,  column  r,  is  computed 
from  the  expression : — 


By  the  addition  of  J  S  and  -£-,  respectively,  to  the  declination  and  annual  variation 

\\J\J 

at  the  head  of  the  table  for  each  star  ("  Details  of  Corrections,"  etc.),  we  derive  the 
definitive  values  of  those  quantities  given  on  the  right-hand  pages  of  the  catalogue. 

The  probable  errors  there  given  do  not  result  from  the  sums  of  squares  of  resid- 
uals, but  are  computed  from  the  weights  of  dd  and  J//;  assuming  the  probable  error  of 
the  unit  to  be  ±  .30.  A  few  trials  showed  that  these  probable  errors  are  a  little  larger, 
on  the  average,  than  those  which  actually  result  from  the  sums  of  squares  of  r,.  In 
deriving  these  sums  accurately  the  full  weight  must  be  given  to  each  of  the  catalogues 
of  the  Brussels,  Paris,  and  Greenwich  series,  though  as  explained  (note  3,  p.  102), 
less  than  the  tabular  values  of  the  weights  are  sometimes  assigned  to  them. 

For  the  fundamental  and  principal  circumpolar  stars,  the  probable  error  of  the 
unit  of  weight,  as  it  actually  results  from  the  residuals  of  each  star,  is  given  below. 
It  will  be  seen  that  in  the  mean  it  is  much  smaller  than  the  standard,  ±  ".30,  to  which 
it  should  correspond.  The  difference  is  not  so  great  for  the  remaining  stars. 


Probable  errors  of  unit  of  n,  derived  from  values  ofrr 


a  Andromedas  ..  i  .24 

a  Oriouis-  .._...  i  .  27 

(3  Ursa?  Minoris     .  i  .Si8 

y  Pegasi  .31 

(3  Gem  i  uorum  ...       .23 

a  Coronse  Borealis      .  26 

a  Cassiopese  25 

a  Hydne  29 

a  Serpentis  ....          .26 

a  Cygui    .                 25 

a  Arietis    .                .  23 

a  Cephei                    24 

a  Ceti  25 

a  UrsfB  Majoris  .       .  29 

77  Dracoois                      24 

(3  Cephei                  .24 

a  Persei                       28 

(3  Leon  is                      23 

a  Tauri  30 

y  Ursse  Majoris  .       .  31 

a  Ophiuchi.           .       .24 

a  Aurigte  27 

a  Virginia  ......       .27 

y  Draconis  ...     .       .  26 

y  Cephei  .   .              30 

(3  Orionis  23 

71  TJrsae  Majoris  .       .  29 

a  Lyrse  25 

/?  Tauri  24 

a  Bootis  ........       .24 

y  Aquihn  ....             .22 

It  must  be  understood,  of  course,  that  the  uncertainty  of  the  Formal  System  is  not 
represented  in  these  probable  errors.  This  uncertainty  will  vary  with  the  polar  dis- 
tance, being  least  at  the  north  pole  of  the  heavens,  and  probably  greatest  in  the  zone 
—  20°  to  —  50° declination,  or  in  that  vicinity.  From  —  30°  to  —  90°,  with  our  present 
means  of  information,  very  little  can  bo  known  of  the  systematic  corrections  required. 
But  northward,  from  —  10°  declination,  we  can  form  an  approximate  judgment  as  to 
the  degree  of  accuracy  attained.  I  estimate  the  probable  error  for  1875  of  the  Normal 
System  for  the  Equatorial  region  to  be  not  greater  than  ±  ".15,  and  less  than  this  for 
any  given  point  between  the  Equator  and  the  North  Pole.  By  actual  computation, 
using  the  Equatorial  systematic  corrections  of  the  32  catalogues  upon  which  the  sys- 
tem is  based,  with  the  same  weights  as  were  used  in  Section  VI.,  we  find  that  the 
system  best  corresponds  to  1847.5.  For  that  epoch  its  probable  error  is  ±  ".05.  For 
1875  it  is  ±  .10;  and  for  1900,  i  ".17.  But  these  probable  errors  may  be  somewhat 


570          UNITED  STATES  NORTHERN   BOUNDARY  COMMISSION.         [1G4| 

too  small  siuce  more  than  half  the  determinations  are  reduced  with  the  same  refrac- 
tions (Bessel's),  and  only  five*  may  be  regarded  as  fundamental  determinations  iu  a 
rigorous  sense. 

It  would  have  been  for  me  a  pleasant  task  to  have  undertaken,  with  the  help  of  the 
places  now  available,  a  third  approximation  to  the  systematic  corrections  and  weights. 
But  the  real  object  of  the  work  has  been  already  sufficiently  accomplished,  and  the 
time  is  not  at  my  disposal  for  the  purpose.  Indeed,  some  few  experiments  taught  me 
that  the  changes  to  be  thereby  induced  were  likely  to  be  few  and  unimportant,  except 
for  some  of  the  weights,  for  which  the  relation  to  number  of  observations  can  now  be 
ascertained  with  considerable  precision.  The  systematic  correction  of  one  catalogue, 
Po  1800,  has,  however,  received  a  new  examination,  the  results  of  which  have  already 
been  given. 

SECTION  IX. 

COERECTIONS  TO  CATALOGUES  OF  CLASS  III. 

There  are  a  few  additional  catalogues  either  of  small  weight,  or  with  few  observa- 
tions of  standard  stars  (described  under  Glass  III),  which  will  prove  desirable  auxil- 
iaries in  the  computation  of  Ad  and  AH'  for  the  remaining  62  stars. 

These  we  proceed  to  enumerate,  and  under  each  will  be  given  a  brief  examination 
of  the  systematic  correction  required. 

The  corrections  to  the  catalogue  declinations  were  found  by  subtracting  from  the 
definitive  A  S'  for  the  required  epoch  the  corresponding  value  of  C. 

Ms  35. 

Weight  one  is  assigned  to  all  declinations,  which  at  Madras  depend  on  more  than 
5  observations,  and  for  which  the  weight  of  a  standard  declination  at  1875  is  1.5,  or 
more.  To  all  declinations,  from  two  or  three  observations  at  Madras,  weight  .5  is 
assigned ;  and  the  same  weight  to  a  few  others  from  four  or  five  observations. 

•These  are:  Bessel's,  1821 ;  Shruve's,  1824  ;  Argelander's,  1829;  Peter's  and  Gylden's  (Ponlkova), 
1845;  and  Kaiser's,  1867. 


[165]  EEPOET  OF  THE  CHIEF  ASTEONOMEE,  APPENDIX  H.  571 

Residuals  in  order  of  declination. 


Mean  6 

•K> 

>'o 

Co 

o 

// 

// 

+  86 

5 

+  .43 

+  .54 

+  78 

8 

+  .62 

+  .62 

+  73 

10 

+  .92 

+  .67 

+  69 

15 

+  .78 

+  .69 

+  64 

12 

+  .41 

+  .64 

+  59 

22 

+  .44 

+  .60 

+  54 

14 

+  .59 

+  .62 

+  49 

27 

+  .80 

+  .72 

+  44 

20 

+  .71 

+  .70 

+  39 

30 

+  .47 

+  .59 

+  34 

17 

+  .06 

+  .44 

+  30 

21 

+  .69 

+  .26 

+  26 

22 

—  .05 

+  .04 

+  21 

24 

—  .28 

—  .26 

+  16 

19 

—  .88 

—  .53 

+  11 

14 

—  .50 

—  .66 

+  6 

20 

—  .42 

—  .67 

+  1 

11 

—  .88 

—  .62 

—  5 

7 

—  .37 

—  .57 

—  9 

11 

—  .72 

—  .51 

—  14 

5 

—  .42 

—  .42 

—  19 

5 

00 

—  .32 

—  23 

5 

+  .68 

—  .22 

-  28 

5 

—  .99 

—  .10 

—  ?5 

2 

+  .70 

+  .05 

—  42 

5 

+  .18 

+  .20 

—  50 

2 

+  .45 

+  .40 

—  59 

6 

+  .54 

+  .62 

—  69 

roi 

F+  .531 

L  v  J 

1   1   •  v"  J 

Three  hundred   and  thirty-two  residuals,  from  —  35°  to  +  90°,  which  received 
weight  one,  give,  with  m  =  8: — 

E  =  ±  ".62. 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

+  15°  to  +  90° 

+  15°  to  —  35° 

—  35°  to  +90° 

Mean  a 

7T7 

ro' 

•K1 

ro' 

TT' 

r»' 

A. 

// 

II 

n 

1 

28 

—  .26 

6 

—  .45 

34 

—  .29 

3 

22 

—  .34 

7 

+  .14 

29 

—  .32 

5 

19 

—  .14 

7 

+  .31 

26 

—  .02 

7 

15 

+  .07 

3 

—  .07 

18 

+  .05 

9 

13 

.00 

6 

—  .25 

19 

—  .08 

11 

16 

—  .39 

8 

+  .08 

24 

—  .24 

13 

13 

—  .39 

5 

—  .02 

18 

—  .09 

15 

26 

+  .78 

7 

+  .89 

33 

+  .80 

17 

30 

+  .49 

8 

+  .16 

38 

+  .42 

19 

25 

-  .12 

13 

+  .14 

38 

—  .03 

21 

33 

—  .38 

13 

—  .08 

46 

—  .30 

23 

23 

—  .18 

11 

—  .11 

34 

—  .15 

572  UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.         [16GJ 


Wn  48  (prime  vertical  transit). 
Sixty-one  observations  in  1847  of  13  stars  gave  as  the  mean  correction: — 

—  ".82  ±".09. 
The  probable  error,  E,  of  a  single  observation,  is  ±  ".70. 

Ms  50. 

The  correction  is  ascertained  from  the  declinations  of  the  principal  stars  given  in 
the  introduction.    Each  residual  is  given  weight  oue. 

Residuals  in  order  of  declination. 


Mean  6 

71-' 

fo 

Co 

o 

// 

// 

+  87 

5 

+  .10 

+  .06 

-+•75 

4 

+  .37 

4-  .25 

+  63 

2 

+  .54 

+  .30 

+  52 

8 

+  .16 

4-  .30 

+  41 

5 

4-  .37 

+  .23 

+  29 
+  22 

8 
8 

—  .06 
—  .41 

—  .08 
-  .40 

+  14 

8 

—  .96 

—  .13 

+  08 

9 

—  .64 

—  .93 

0 

7 

—1.17 

—1.05 

—    9 

6 

—  .99 

—  .99 

With  m  =  4,  we  have,  probable  error  of  a  single  declination  :— 

E  =  ±  ".32. 

If  we  assume  -  =  2,  we  shall  have  for  3  to  5  observations,  approximately,  weight 
.3  in  the  system  of  Table  XI. 

Residuals  in  order  of  right  ascension. 


Mean  re 

TT' 

n/ 

Mean  a 

7T- 

ro' 

h. 

// 

k. 

II 

1 

5 

—  .17 

13 

4 

.00 

3 

5 

—  .20 

15 

7 

4-  .19 

5 

(i 

—  .29 

17 

6 

—  .01 

7 

5 

4-  .28 

19 

9 

+  .35 

9 

5 

—  .37 

21 

8 

+  .40 

11 

5 

—  .34 

23 

4 

—  .26 

REPORT  OP  THE  CHIEF  ASTRONOMER,  APPENDIX  H. 


573 


Eh  58,  Eh  63,  and  Eh  67.    -1  =  2. 


Eh  58. 

Eh  63. 

Eh  67. 

Mean  rf 

TT' 

ro 

Co 

Mean  <i 

V 

ra 

Co 

Mean  <5 

ir7 

r0 

Co 

o 

n 

// 

o 

it 

II 

0 

n 

II 

+  89 

4 

—.63 

+  89 

2 

—  .40 

+  89 

2 

+  .86 

4-  73 

3 

—.94 

+  73 

1 

+.27 

+  67 

5 

+1  34 

+  55 

20 

+.06 

-.33 

+  55 

19 

+.37 

+.51 

+  54 

16 

+  .38 

00 

-f  32 

26 

—.52 

—.33 

+  32 

20 

+.35 

+.51 

+  32 

18 

—  .45 

00 

-t-  19 

26 

+.53 

—.33 

+  19 

30 

+.72 

+.51 

+  19 

28 

+  .50 

00 

+    7 

31 

—.36 

—.33 

+    9 

18 

+.59 

+.51 

+  07 

17 

+  .61 

00 

—    5 

37 

—.22 

—  .  3:1. 

I 

14 

+.39 

+.51 

+  05 

17 

—1.30 

00 

The  correctious  to  these  catalogues  can  only  be  roughly  ascertained.  It  is  assumed 
to  be  constant  from  —  10°  to  +  60°.  We  have,  E  =  ±  ".GO  for  Eh  58  (excluding  /3 
Lyra),  ±  ".77  for  Eh  63,  and  ±  1".33  for  Eh  67.  ±  ".69  is  adopted  in  constructing 
weights  for  Eh  58  and  Eh  63. 

Pa  62  (prime  vertical  transit). 

Twenty-one  observations  of  5  stars  give  the  correction : — 

+  ".25  ±  ".05 ; 

and  for  probable  error  of  single  observation  ±  ''.23,  which  is  considerably  larger  than 
the  value  supposed  in  the  third  volume  of  Poulkova  observations  (pp.  213,  214).  But 
even  this  requires  the  maximum  weight  (5.0)  for  3  observations,  and  is  adopted. 

Pa  71. 

But  one  declination  is  used  from  this  catalogue — that  given  for  B.  A.  C.  5313. 
For  its  correction,  I  find  +  ".50  from  eight  stars  between  +  50°  and  +  CO0  declination. 
For  this  declination  the  arbitrary  weight  1.0  is  assigned  in  deducing  corrections  to 
assumed  place. 

Wn  70. 

Residuals  in  order  of  declination. 


Mean  S 

JT* 

» 

Co 

o 

,, 

II 

+  86 

21 

+  .22 

00 

£ 

+  75 

57 

—  .04 

00 

^~=2 

+  65 

67 

—  .43 

—  .25 

' 

+  55 

17 

+  .19 

—  .43 

+  45 

31 

—  .6:! 

—  .57 

+  35 

20 

—  .44 

—  .66 

+  -5 

33 

—  .72 

—  .73 

+  15 

24 

—  .42 

—  .75 

+  05 

29 

—1.08 

—  .70 

—  07 

14 

—  .05 

-  .36 

574          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 

With  m  =  4,  we  have  :  — 

E  =  ±  r'.oi. 


[108] 


The  curve  resembles  that  of  Wn  56  closely,  except  that  its  minus  values  are  about 
".40  larger.  From  —  10°  southward,  Wu  56  —  ".40  can  probably  be  used  without 
serious  error. 

Residuals  in  order  of  right  ascension. 


Declination  limits. 

Declination  limits. 

Declination  limits. 

—  10°  to  +  40° 

+  40°  to  +90° 

—  10°  to  +90° 

Mean  a 

TT' 

ra' 

TT' 

n>' 

if 

w 

Co' 

ft. 

II 

// 

II 

// 

1 

11 

+  .21 

25 

—  .14 

36 

—  .04 

—  .17 

3 

12 

+  .02 

15 

—  .59 

27 

—  .32 

—  .23 

5 

4 

—  .75 

13 

—  .77 

17 

-  .76 

—  .24 

7 

14 

4-  .09 

5 

—  .30 

19 

—  .01 

—  .18 

9 

9 

-!-  .20 

11 

—  .21 

20 

—  .03 

—  .07 

11 

4 

—  .75 

15 

—  .29 

19 

—  .38 

4-  .06 

13 

9 

—  .36 

15 

—  .23 

24 

—  .28 

4-  .17 

15 

6 

+  .70 

19 

+  .80 

25 

4-  .78 

4-  .23 

17 

12 

+  .60 

20 

4-  .33 

32 

+  .43 

4-  .24 

19 

15 

—  .78 

17 

+  .26 

32 

—  .23 

4-  .18 

21 

16 

4-  .35 

21 

4-  .04 

37 

4-  .18 

4-  .07 

23 

12 

—  .26 

18 

—  .16 

30 

—  .20 

-.06 

Column  GO'  is  taken  from  the  correction  found  to  be  applicable  to  the  previous 
series  of  observations  with  the  Washington  mural  circle.  There  is  sufficient  resem- 
blance between  it  and  the  values  of  r0'  iu  the  last  column  to  justify  its  continued  use 
for  this  catalogue. 

TABLE  XII. — Corrections  to  catalogues  of  Class  III  (and  to  Po  1800). 
ORDER  OF  DECLINATION. 


Mean  6 

PolSOO 

Ms  £>. 

Ms  50. 

Wn  70.* 

Mean  6 

Po  1800. 

Ms  35. 

Ms  50. 

Wn70. 

o 

// 

n 

// 

II 

o 

// 

a 

It 

It 

4-  90 

00 

+  .50 

00 

00 

4-  15 

—1.62 

—  .56 

—  .70 

—  .75 

4-85 

4-  -16 

+  .55 

4-  .10 

00 

+  10 

—1.  35 

—  .68 

—  .86 

—  .75 

4-  80 

4-  .30 

4-  .60 

4-  .20 

00 

4-  05 

—1.29 

—  .67 

—1.00 

—  .70 

4-75 

4-  .44 

4-  .65 

+  .25 

00 

0 

—1.56 

-  .61 

—1.05 

—  .59 

4-70 

4-  .52 

4-  .70 

4-  .30 

—  .14 

-  03 

—  1.  86 

—  .57 

—  1.  C5 

—  .44 

4-  65 

4-  .52 

4-  .65 

4-  .30 

—  .25 

—  10 

—1.96 

—  .50 

—  .97 

—  .25 

4-  60 

4-  .48 

4-  .60 

4-  .30 

—  .37 

—  15 

—1.82 

—  .40 

4-  55 

4-  .35 

4-  .60 

4-  .30 

—  .43 

—  20 

—1.5(1 

—  .30 

4-  50 

4-  .10 

4-  .72 

4-  .30 

—  .50 

—  25 

—  1.16 

—  .17 

4-  45 

—  .30 

4-  .72 

4-  .28 

—  .57 

—  30 

—1.08 

—  .05 

4-  40 

—  .80 

4-  .62 

4-  .22 

—  .62 

—  35 

—1.21 

4-  .05 

4-  35 

—1.03 

+  .48 

4-  .10 

—  .66 

—  40 

—1.40 

4-  .15 

4-  30 

—1.10 

4-  .26 

—  .04 

—  .70 

—  50 

4-  .40 

4-  25 

—1.33 

-.02 

—  .26 

«*3 

—  60 

4-  .65 

+  20 

—1.62 

—  .32 

—  .49 

—  .75 

"  If  the  ac'ual  correction  for  Wn  1872  and  1873  is  desired, 
given  in  the  above  table  for  Wn  70. 


".45  must  be  added  to  the  quantities 


[169]  KBPOET  OF  THE  CHIEF  ASTBONOMEB,  APPENDIX  H.          575 

TABLE  XII.— Continued. 


Catalogue. 

Correction. 

Remarks. 

Wn  48  

// 
—  .82 

Constant. 

Eh  58  

—  .S3 

Constant  from  —  10°  to  -f-  60°. 

Eh  63  

-t-  .51 

Constant  from  —  10°  to  +  60°. 

Pa  62  

+  .25 

Constant. 

Eh  67  

00 

Constant  from  —  10°  to  +  60°. 

The  corrections  in  order  of  a  for  Po  1800  and  Wn  70  are  to  be  taken  from  Table  X. 

With  these  additional  corrections  the  values  of  A  8  and  A  /j.'  were  computed  for  the 
62  remaining  stars.  These  are  sufficiently  indicated  in  the  "Details  of  Corrections 
to  Assumed  Declinations"  by  the  use  of  one  or  more  of  the  catalogues  of  Class  III. 

SECTION  X. 

GENERAL  REMARKS  RESPECTING  THE  CORRECTIONS  AND  PROBABLE  ERRORS  OF 
STARS  USED  BY  THE  NORTHERN  BOUNDARY  SURVEY  FOR  LATITUDE. 

The  preceding  pages  afford  the  means,  to  some  extent,  for  answering  the  question 
as  to  the  probable  errors  of  the  declinations  used  in  latitude  work  on  the  Northern 
Boundary.  These  declinations  in  the  general  catalogue  of  500  stars  at  the  end  of  this 
paper  are  distinguished  by  an  asterisk,  affixed  to  the  current  number.  Opposite  each 
star,  on  the  right-hand  page  (and  in  the  third  column),  will  be  found  its  probable  error 
estimated  in  the  manner  described  in  Section  VIII.  This,  taken  together  with  the  cor- 
responding value  of  J5,  given  on  the  left-hand  page,  will  aid  informing  some  judgment 
as  to  the  probable  limits  within  which  any  correction  is  likely  to  be  included.  These 
values  of  A5  refer  to  the  declinations  adopted  in  the  work  of  1874.  Those  of  the  pre- 
ceding years  are  less  accurate,  and  differ  slightly  from  these,  but  the  differences  are  not 
systematic. 

The  general  correction  required  by  the  latitude  work  of  1874  has  been  roughly 
computed  in  three  different  ways: — 

First.  Fifty  different  pairs  (100  stars)  were  observed  for  latitude  during  the  year. 
Six  of  these,  however,  were  used  but  once;  one,  three  times;  three,  four  times;  nine, 
live  times;  and  others  more  frequently — eighteen  times  being  the  maximum.  Taking 
the  simple  mean  of  all  the  values  of  A  S  for  the  one  hundred  stars,  we  have: — 

+  ".042 

as  the  common  correction  to  the  declinations  actually  used ;  and  this  is,  of  course, 
applicable  to  the  latitudes. 

8ec:>nd.  If,  however,  we  take  into  account  the  number  of  times  each  pair  was  used, 
giving  weights  proportional  to  the  numbers,  we  have: — 

+  ".OG8 

as  the  common  correction  to  all  the  latitudes. 

Third.  If,  still  further,  we  take  into  account  the  weights  of  the  stars  as  computed 
in  this  paper,  and  if  we  suppose  that  each  observation  of  a  pair  with  the  zenith  tele- 


576          UNITED  STATES  NORTHERN   BOUNDARY  COMMISSION.         [170| 

scope  gives  an  instrumental  probable  error  for  latitude  of  ±  ".3,  we  have  as  the  mean 
correction : — 

+  ".OO3. 

I  regard  it  as  quite  improbable  that  a  common  correction  larger  than  i  ".1  is 
needed  for  the  latitudes  as  actually  established  in  the  field.  In  this  paper  the  stars  of 
the  latitude  list  were  reduced  without  the  slightest  reference  to  the  previous  work 
performed  on  them— even  the  seconds  of  declinations  being  transcribed  from  the  vari- 
ous catalogues  anew.  Under  these  circumstances  the  present  work  may  be  regarded 
as  an  efficient  check  on  the  values  of  declination  adopted  in  the  former  discussion. 

EXPLANATION  OF  TABLES. 

RECAPITULATION  OP   SYSTEMATIC  CORRECTIONS. 

This  table  shows  as  nearly  as  possible  the  total  systematic  corrections  applied  by 
me  (either  before  or  after  discussion  of  Normal  System)  to  the  catalogue  places  as  I  find 
them.  If  to  these  be  added  errata  and  corrections  due  to  proper  motion,  with  a  few 
corrections  specified  in  the  notes  at  the  end  of  the  table,  we  shall  have  declinations 
according  to  the  system  adopted  in  this  paper.  In  order,  however,  to  accertain  the 
degree  of  confidence  to  be  placed  in  certain  values  from  the  curves  (especially  those 
from  —  10°  to  —  30°),  it  will  be  necessary  to  recur  to  the  detailed  reductions. 

DETAILS  OP  CORRECTIONS  TO  ASSUMED  DECLINATIONS. 

These  embrace  Table  A,  Table  B,  and  Table  C. 

Table  A  contains  particulars  of  reduction  for  the  fundamental  and  principal  cir- 
cumpolar  stars.  However,  four  southern  stars,  usually  regarded  as  fundamental,  and 
a2  Gemiuorum  will  be  found  elsewhere. 

Table  B  contains  details  for  all  other  stars  (i.  e.,  stars  not  included  in  Table  A) 
situated  between  +90°  and  —10°  declination.  In  this  region  the  weights  are  in  no 
case  affected  by  the  question  of  zenith  distance. 

Table  C  contains  details  for  all  stars  situated  south  of  —  10°  declination. 

With  one  exception  the  construction  of  all  the  tables  is  alike.  At  the  head  of 
the  tabular  statement  for  each  star  is  given  its  assumed  right  ascension  and  declina- 
tion, with  the  annual  variation  of  each  as  computed  in  Sections  II.  and  III. 

Column  "  Cat."  contains  the  designation  of  each  catalogue  or  series  of  observa- 
tions. The  explanation  of  these  designations  is  found  in  Section  IV.  It  is  sufficient 
here  to  state  that  the  figures  refer  to  the  mean  year  of  observation,  and  the  letters  are 
usually  the  first  and  last  in  the  name  of  the  observatory  according  to  the  English 
spelling. 

Column  "  Obs."  contains  either  the  number  of  observations,  weight,  or  probable 
error,  according  as  either  is  made  an  argument  for  computation  of  weight  from  Table 
XI. 

Column  C  contains  the  correction  to  assumed  declination  given  by  the  respective 
catalogues  in  the  manner  detailed  in  Sections  III.  and  V.  For  the  later  Iladcliffe  cat- 
alogues, and  for  Wn  72,  values  of  C  are  contained  in  Section  V. 


[171]  EEPOET  OF  THE  CHIEF  ASTRONOMER,  APPENDIX  H.          577 

Column  Gn  in  Tables  B  and  C,  contains  for  a  limited  number  of  stars  the  sum  of 
C  and  of  the  systematic  correction  taken  from  Table  II. 

The  place  of  this  is  supplied  in  Table  A  by  column  r/t,  which  contains  the  correc- 
tion given  to  each  authority  by  the  declination  computed  according  to  the  principles  of 
Section  VI.,  but  with  the  addition  of  the  Fundamenta  as  an  authority,  with  weight 
one. 

Column  r  contains  the  quantities  from  which  definitive  systematic  corrections 
were  computed.  It  is  formed  by  subtracting  C  from  the  value  of  the  expression 


J5  +  (T'~  ]^)  ^V)  J  5  an(1  -V  being  taken  fr°m  Tables  V.  and  VII. 

Column  C,,  is  formed  by  the  addition  of  the  systematic  corrections  of  Tables  IX. 
and  X.  to  column  G.  For  Re  66  and  Re  72,  as  well  as  Wn  72  and  S  H  31,  the  value  of 
C,,  is  specially  computed. 

Column  TT  contains  the  weight  computed  from  Table  XI.,  with  the  argument  in 
column  "Obs." 

Column   r,  contains  the  outstanding   residual    found    by   subtracting  C,,  from 


s  rr\  _  1S75\ 

AS  +  dp!C-  -  J,  where  AS  and  J/t'  are  to  be  taken  from  the  left-hand  page  of 

the  "Catalogue  of  500  Stars"  at  the  end  of  this  paper. 

CATALOGUE  OF  500  STABS. 

On  the  left-hand  page  : 

Columns  1,  2,  3,  and  4  appear  to  require  no  explanation  except  the  caution  that 
the  latter  column  is  simply  copied  from  the  catalogue  of  the  British  Association. 

Column  5  contains  the  approximate  right  ascension  as  deduced  in  Section  VII. 

Column  6  contains  the  annual  variation,  and  column  7  the  secular  variation  in 
Right  Ascension  given  in  units  of  the  fifth  decimal  place. 

The  eighth  and  ninth  columns  give  A  8  and  A  p.'  as  they  result  from  the  final  com- 
putation, using  columns  C,,  and  K  of  "Details,"  etc. 

On  the  right-hand  page,  in  column  1,  the  current  number  is  repeated  for  con- 
venience. 

Column  2  is  the  definitive  declination  formed  from  the  assumed  declination  given 
with  each  star  in  "Details,"  etc.,  by  the  addition  of  Ad  from  the  preceding  page. 

Column  3  contains  the  probable  error  ascertained  in  the  manner  explained  near  the 
end  of  Section  VIII.  In  a  few  cases  this  column  is  left  blank.  It  is  to  be  understood 
in  such  cases  that  a  definite  estimate  is  declined,  either  because  the  error  is  large  or 
cannot  readily  be  ascertained. 

Column  4  contains  the  weight  to  nearest  unit,  from  which  the  preceding  column  is 
estimated.  The  probable  error  of  this  unit  is  supposed  to  be  uniformly  ±  ".30.  It  is 
likely  to  be  smaller  than  larger  (p.  1C3).  When  this  column  is  left  blank  it  ia  to  be 
understood  that  the  computed  weight  is  less  than  .5 

Column  5  contains  the  definitive  annual  variation,  computed  by  adding  to  the 

A      I 

annual  variation  of  "Details,"  etc.,  -£-;  Ay!  being  taken  from  the  left-hand  page. 


578          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.         [172] 

Column  6  contains  the  probable  error  of  the  annual  variation  computed  from  the 
weight  of  J/t'  iii  conditional  equations. 

Columns  7  and  8  contain  the  secular  variation  and  third  term  of  precession  in 
declination  which  are  given  respectively  to  the  sixth  and  eighth  places  of  decimals. 
The  mode  of  their  computation  is  fully  explained  in  Section  III. 

Column  9  contains  the  proper  motion  formed  by  subtracting  from  the  annual 
variations  20".0542  cos  a.  The  number  is  Peters'  constant  of  precession  (n)  for  1875. 


RECAPITULATION 


Of 


SYSTEMATIC  COBRECTIONS  TO  DECLINATIONS. 


[173]  579 


RECAPITULATION  OF  SYSTEMATIC  CORRECTIONS. 


i 

r-t 
O 
M 

o 
t—  i 

30 

K 

IO 

Q 

H 

bo 
« 

i 

v 
ea 

-«  ^3 

(N   5 

so 

M 

s 

a 
O 

5 

sS 

^r  o 

c*co 

4B 

Q 

si 

; 

gj 

0 

<! 

ti 

§ 

cc 

w 
o 
d 

6 

0 

4-  90 

"oo 

"oo 

"oo 

"oo 

// 

"oo 

// 

"oo 

// 
4-  .  10 

a 

o 
4-  90 

_j_  35 

4-     16 

4-     14 

4-    03 

4-  .04 

—  .05 

00 

4-  .  12 

4-  85 

-4-  80 

4-     30 

4-     29 

+  .06 

4-  .11 

—  .12 

00 

4-  .15 

4-  80 

4-  75 

4-     44 

4-    38 

4-  .  10 

4-  .20 

—  .17 

4-  .40 

00 

4-  .15 

+  75 

-1-  TO 

+     52 

4-    30 

4-  .13 

4-  .28 

—  .21 

4-  .40 

00 

4-  .13 

4-  70 

4-  G5 

4-  GO 

4-  .52 
4-     48 

+  -14 
02 

+  .16 

4*  .18 

4-  .36 
4-  .43 



—  .24 
—  .26 

4-  .40 
4-  .40 

00 
00 

4-  .08 
00 



4-  65 
4-  60 

_|_  55 

4-     35 

01 

4-  .16 

4-  .46 

—  .27 

4-  .38 

00 

—  .12 

4-  55 

4-  50 

4-     10 

4-     12 

4-     13 

4-  .48 

—  .25 

4-  .31 

—  .02 

—  .31 

4-  50 

+  45 

30 

4-     10 

4-  .09 

4-  .49 

—    22 

4-  .24 

.07 

—  .54 

4-  45 

+•40 

BO 

00 

4-  .06 

4-  .51 

00 

—  .19 

+  -I7 

—  .  13 

—  .76 

4-  40 

4-  35 

—1.03 

4-  .06 

4-  .56 

00 

—  .15 

4-  .07 

—  .18 

-  .95 

4-  35 

4-  30 

1  10 

4-    06 

4-  .61 

00 

—  .13 

—  .03 

—  .22 

—1.12 

4-  30 

+  '2T> 

1  36 

4-     07 

4-  .60 

00 

—  .12 

—  .16 

—  .25 

—1.24 

4-  25 

4-  20 

—1  62 

4-  .10 

+  -74 

CO 

—  .15 

—  .20 

—  .29 

—1.30 

4-  20 

4.  15 

—1  62 

4-  .13 

+  .81 

CO 

—  .21 

—  .17 

—  .32 

—1.31 

+  15 

4.  10 

—1  35 

4-  .  16 

4-  .88 

00 

—  .29 

—  .14 

—  .36 

—1.31 

4-  .35 

+  10 

4-     5 

—1  29 

4-  .19 

4-  .95 

00 

—  .38 

—  .10 

—  .43 

—1.  33 

4-  .35 

+    5 

0 
5 

—1.56 
—1  86 



+  .25 
4-  .33 

4-1.04 
4-1.15 

00 
00 

—  .49 

—  .60 

—  .07 
—  .03 

—  .52 
—  .60 

—1.37 
—  1.49 

4-  .35 

4-  .35 

0 
—    5 

—  10 

—1  96 

4-  .43 

4-1.31 

00 

—  .72 

00 

—  .68 

—1.68 

4-  .35 

—  10 

15 

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[175J 


When  the  argument  is  12b  to  24h  the  signs  are  to  bo  reversed. 


.r:8l 


582 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[176] 


Recapitulation  of  systematic  corrections — Continued. 


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J177] 


RECAPITULATION  OF  SYSTEMATIC  CORRECTIONS. 


583 


Recapitulation  of  systematic  corrections—  Continued. 


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584 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.         [178J 


Recapitulation  of  systematic  corrections — Continued. 


6 

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1 179] 


RECAPITULATION  OF  SYSTEMATIC  CORRECTIONS. 


585 


Recapitulation  of  systematic  corrections — Continued. 


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When  the  argument  is  12h  to  24h  the  signs  are  to  be  reversed. 


586          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.          [180] 


Recapitulation  of  systematic  corrections — Continued. 


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[181] 


RECAPITULATION  OF  SYSTEMATIC  CORRECTIONS. 


587 


Recapitulation  of  systematic  corrections — Continued. 


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When  the  argument  is  12'  to  24h  tbe  signs  are  to  be  reversed. 


588         UNITED  STATES  NOETHEEN  BOUNDAEY  COMMISSION.          [182] 


Recapitulation  of  systematic  corrections — Continued. 


6 

Wn  70,  tran- 
sit circle.  (/i) 

Wn  71  and 
Wn  72,  tran- 
sit circle.(A) 

1! 

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—  .70 

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—  .80 
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+  80 

+  75 
+  70 
+  65 

+  60 
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22 

11 

23 

12 

24 

When  the  nrgnment  is  12h  to  24h  the  signs  are  to  be  reversed- 


[183] 


RECAPITULATION  OF  SYSTEMATIC  CORRECTIONS. 


589 


Recapitulation  of  systematic  corrections — Continued. 


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8 

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+  60 
+  55 
+  50 

+  45 
+  40 
+  35 

+  30 
+  25 
+  20 

+  15 

+  10 

+    5 
0 
—    5 
—  10 

—  15 
—  20 
—  25 

—  30 
—  35 

+  :'io 

+  .27 
+  .38 

+  .41 
+  .40 
+  .31 

+  .20 
+  .08 
—  .03 

—  .10 
—  .14 
—  .18 

—  .18 
—  .18 
—  .21 

—  .33 
—  .42 
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+  .40 
+  .53 

+  .62 

+  .80 
+  .90 

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+1.43 
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+1.21 
+  .96 
+  .60 

+  .47 

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—  .88 
—1.06 
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—  .93 
—  .91 
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—  .66 
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—  .65 
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+  .24 
+  .32 

+  .40 
+  .48 
+  .50 

+  .51 
+  .49 
+  .42 

+  .33 
+  .15 
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—  .21 
—  .17 

+  .08 

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+  .44 
+  .40 

+  .30 

+  .18 
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—  .11 

—  .20 

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+  .39 

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+  .67 
+  .80 

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+  .82 
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—  .06 
+  .10 

+  .21 
+  .23 
+  .11 

—  .09 
—  .26 
—  .34 

—  .  35 
—  .30 

—  .25 

—  .20 

o 
+  90 
+  85 
+  80 

+  75 
+  70 
+  65 

+  60 
+  55 
+  50 

+  45 
+  40 
+  35 

+  30 
+  25 
+  20 

+  10 
+  15 

+    5 

0 
—    5 
—  10 

—  15 

—  20 
—  25 

—  30 
—  35 

—  40 

—  40 

—  50 

—  50 

—  60 

60 

—  70 

—  70 

—  80 

—  80 

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—  90 

A.R. 

ti 

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g 

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3 

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1 

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2 

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4 

16 

5 

17 

6 

18 

7 

19 

8 

20 

9 

21 

10 

22 

11 

23 

12 

24 

When  the  argument  is  121"  to  24h  tbe  signs  are  to  be  reversed. 

For  general  explanation  see  Sections  VIII.  and  X. 

Notes. — In  a  few  cases  the  corrections  of  the  table  are  only  applicable  to  declinations  by  direct  obser- 
vations above  the  pole.  For  these,  whore  it  is  thought  to  be  worth  while,  the  corrections  to  declina- 
tions, as  they  result  from  observations  below  the  pole,  are  given  in  the  following  table. 


590          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.          [184] 

For  observations  below  the  pole. 


A 

Ce  36  and 
Ce37. 

Eh  41. 

Eh  42. 

Eh  43. 

Eh  44. 

Wn45. 

Ce  45  to 
Ce51. 

Wn  61  and 
Wn62. 

d 

o 

n 

// 

// 

n 

// 

n 

// 

// 

o 

+  90 

+  .09 

—  .23 

+  .94 

—1.29 

+  .36 

+  .35 

+  .43 

+  .76 

+  90 

+  85 

+  .09 

—  .17 

+1.06 

—1.36 

+  .37 

+  .39 

+  .43 

+  .79 

+  85 

+  80 

+  .09 

+  .01 

+1.16 

—1.39 

+  .37 

+  .40 

+  .43 

+  .80 

+  80 

+  75 

+  .09 

+  .13 

+1.24 

—1.37 

+  .34 

+  .39 

+  75 

+  70 

+  .0-2 

+  .35 

j_  70 

+  65 

—  .09 

+  65 

-4-  60 

—  .23 

•4-  60 

Washington  transit  circle. 

i 

Wn  65. 

Wn66. 

Wn  67  (be- 
fore June  1). 

Wn  67  (after 
June  1.) 

Wn68. 

Wn69. 

Wn74. 

& 

0 

// 

// 

// 

// 

It 

// 

// 

o 

+  90 

+  .55 

+  .29 

—  .20 

—  .54 

+  .14 

+  .15 

—  .07 

+  90 

+  85 

+  .58 

+  .36 

—  .16 

—  .50 

+  .10 

+  .19 

—  .17 

+  85 

+  80 

+  .59 

+  .44 

—  .11 

—  .45 

+  .07 

+  .25 

—  .28 

+  80 

+  75 

+  .58 

+  .53 

—  .03 

—  .37 

+  .06 

+  .33 

—  .38 

+  75 

+  70 

+  .55 

+  .62 

+  .06 

—  .28 

+  .05 

+  .41 

—  .48 

+  70 

These  corrections  are  in  the  cases  of  Ce  36  to  Ce  37,  Wn  45,  Ce  45  to  Ce  51,  Wn  61  and  Wn  62,  and 
Wn  63  to  Wn  65,  derived  merely  by  the  addition  of  a  constant  to  the  correction  for  declinations  above 
the  pole. 

(a)  Correctional  ultima;,  pp.  351  to  371  of  Strnve's  Pos.  Med.  (1630)  must  be  added  for  each  star  to 
the  correction  of  Dt  24,  in  order  to  make  it  applicable  to  Dt  30. 

(i)  Ee  45.  The  corrections,  with  reversed  signs,  pp.  viii  to  xi  Int.  to  Kadcliffe  catalogue  for  1845 
must  be  added. 

(c)  The  curve  southward  from  —  10°  is  probably  very  near  Ms  35  —  0".4. 

(d)  Ee  58.    The  correction,  pp.  xviii  and  six  Int.  to  second  Radclifife  catalogue,  must  be  added,  with 
reversed  signs. 

(e)  Me  62.    The  important  effect  of  the  correction  given  in  the  table,  pp.  xxii  to  xxiv,  introduction 
to  the  catalogue,  varies  too  rapidly  to  be  included  here.    The  two  corrections  must  therefore  be  added. 

(/)  Observations  taken  from  Bonn  Beob.  Bd.  vi  require  the  further  correction  given  in  Int.,  p.  xiv. 

(j)  The  corrections  to  Wn  66-69  (transit  circle)  are  applicable  to  the  mean  declinations  of  the 
detailed  observations  after  these  have  been  corrected  for  division  error  only.  The  effect  of  the  latter 
might  have  been  included ;  but  greater  accuracy,  in  interpolating,  results  from  the  above  coarse. 

(h)  Applicable  to  declinations  of  the  catalogues. 


CATALOGUE  OF  500  STARS 


FOR 


THE  EPOCH  1875.0, 


CONTAINING  DECLINATIONS  WITH  THEIR  ANNUAL  VARIATIONS  AND  OTHER 

TERMS  OF  PRECESSION. 


COMPILED  FROM  ORIGINAL  AUTHORITIES. 


591 


592 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[186J 


Catalogue  of  500  stars 


Number. 

a 
I 

a 

.  e* 

o_S 

^j 

« 

Name. 

Magnitude. 

Approximate 
right  ascen- 
sion, 1875.0. 

A 

f  rf 

>a 

"«  3 
o  2 
a+3 
a 
•JJ 

<Pa 
d«s 

Ad 

v 

1 

4 

a     Andromeda}  .... 

1 

h.  in.     s. 
.  0  01  55  8 

s. 
+  3  089 

8. 
-L         18 

it 
43 

// 

98 

2 

7 

/?    Cassiopeae  .  

2.5 

02  31.1 

+  3.  162 

-L      54 

07 

4-     81 

3 

26 

•y    Pe^asi  .  . 

2 

06  48.0 

+  3  082 

-L         10 

41 

15 

•4 

46 

6 

10  15.1 

+  3  183 

4-      60 

4-     33 

4-2  24 

"5 

67 

p    Andromeda?  .  

5.5 

14  32.4 

+  3.141 

4-      26 

36 

1  00 

6 

88 

/3    Hydri  

3 

19  09.  1 

+  3.  2C6 

—    154 

11 

1  30 

•7 

120 

6 

24  47.6 

+  3.116 

-L      24 

1  15 

8  30 

8 

126 

K    Cassiopeae  .  

4 

25  54.5 

-f  3  358 

_L      70 

4-    78 

4-     23 

9 

153 

f     CjissiopesB-  .  

4 

30  01.0 

-f-  3  309 

-L      49 

10 

14 

10 

155 

TT    Andromeda}  .....  

4.5 

30  12.5 

+  3  188 

-L      24 

+    98 

+     30 

11 

166 

6    Andromedaj  .  . 

3 

32  38.8 

+  3  192 

-4-      22 

4-    35 

4-1  45 

12 

169 

a     Cassiope®  ..  .  

3 

33  25.5 

+  3  366 

-f-      55 

01 

17 

*13 

175 

6 

34  37.5 

-j-  3  510 

4-      87 

4-    51 

4-1  71' 

14 

196 

(8    Ceti  

?.5 

37  18.8 

+  3  012 

—        6 

03 

4-     49 

15 

194 

21  Cassiopeia  

5.5 

37  25.6 

+  3  834 

+     160 

4-1  11 

4-2  4:! 

•16 

198 

o    Cassiopesa  

5.5 

37  45.9 

+  3  314 

4-      41 

22 

47 

17 

215 

4 

40  43.0 

+  3  169 

-L       18 

4-     79 

+2  72 

18 

218 

4 

41  32.8 

+  3  581 

_L      fi4 

4-     43 

+1  35 

*19 

219 

5 

41  45.5 

-f.  3  367 

-L      4« 

4-    97 

-1-1   34 

*20 

239 

5.5 

45  37  5 

+  3  530 

_L      71 

+     50 

•4-1   44 

21 

253 

}•    Cassiopese  

3 

49  10  7 

+  3  566 

4-      71 

4-    26 

+1  57 

*22 

259 

4 

49  49  2 

+  3  304 

4-      30 

^       o" 

86 

23 

288 

e     Piscium  

4 

56  27  4 

+  3  109 

4-      09 

,   ,    44 

37 

*24 

(LL.  1985) 

I  02  95  9 

_J_    •}    9(JQ 

.    in 

1      60 

i  ]   70 

25 

3:!4 

ft    Andromeda)  

2 

02  44  3 

+  3  340 

4-      29 

•    51 

"  63 

"26 

345 

82  Piscium  

5.5 

04  13  4 

+  3  291 

4-      25 

+     47 

+1  36 

27 

395 

v    Piscium  

5.5 

12  36  0 

+  3  283 

4-      22 

'17 

1  15 

28 

360 

a    Ursaa  Minoris  

2 

13  00  2 

+20  868 

+15068 

+     0-2 

°6 

•29 

401 

91  Piscium  

6 

14  12  9 

+  3  301 

4-      23 

46 

71 

30 

416 

<5     Cassiopeaa  

3 

17  39  3 

+  3  870 

4-      79 

4-     02 

+    34 

31 

420 

61   Ceti  

3 

17  46  5 

+  2  998 

+      02 

4-     01 

,    5'j 

*32 

4:i8 

3d  Cussiopeaj.  

5 

21  57  4 

+  4  357 

+     144 

87 

2  86 

33 

447 

y    Phenicis  

3 

22  56  1 

+  2  612 

13 

48 

3  58 

34 

453 

q     I'isi  iuni  

4 

24  47  7 

+  3  199 

4-       14 

1  15 

2  54 

*35 

474 

B 

28  49  2 

-t-  3  630 

-t-        /IS 

-    9^ 

a_    -if) 

*3G 

487 

51  Andromeda? 

3  5 

30  19  g 

_L  3  64g 

U-        48 

17 

-t-  •••" 
J-    fil 

37 

507 

a    Eridani  . 

1 

33  03  3 

+  2  240 

13 

00 

-f-    .01 

-  1  74 

*38 

522 

54  Andromedse  

4 

35  50  2 

+  3  726 

+       53 

58 

2  49 

39 

537 

o    Piscinm  

5 

33  47  7 

+  3  162 

4-       11 

57 

1  17 

"40 

560 

2    Persei  

6 

44  13  1 

-f-  3  781 

-1-       ^4 

j-    fil 

+     ft1 

41 

564 

e    Cassiopese  

3 

45  25  4 

_|_  4  245 

+      99 

+    09 

.OL 

47 

42 

51  i9 

a    Triangnli  

3  5 

45  57  6 

+  3  40'5 

is 

.     2'{ 

43 

577 

fi    Arietis  

3 

47  44  2 

_j_  3  301 

+       18 

5'3 

+     53 
,    i  40 

44 

600 

50  Cassiopeaa  

4 

52  47  9 

-(-  4  984 

+    186 

+1  06 

[  tj  -ir^ 

»46 

611 

53  Cassiope®  

6 

53  46  4 

_j_  4  3g5 

+      11 

41! 

Q5 

[187J 

for  the  epoch  1875.0. 


CATALOGUE  OF  500  STARS. 


593 


Number. 

Declination,  1875.0. 

Prob.iiblo  error 
of  3,  1875. 

Weight. 

Anunal  varia- 
tion, 1875.0. 

Probable  error 
of  annual  va- 
riation. 

ft 

di" 

<Pc5 
di3 

Proper  motion 
in  i. 

O     '      11 

// 

// 

// 

II 

II 

a 

1 

+  28  24  00.79 

.06 

26 

+  19.8866 

.0021 

—  124 

—  102 

—  .  1669 

2 

+  58  27  36.  63 

.12 

6 

+  19.8601 

.  0030 

—  140 

—  109 

—  .  1929 

3 

-f-  14  29  18.67 

.06 

24 

+  20.  026!) 

.0022 

—  220 

—  101 

—  .  0185 

•4 

-f  GO  50  18.60 

.35 

I 

+  20.0365 

.0102 

—  294 

—  Ill 

+  .  0024 

»5 

+  37  16  33.  11 

.10 

8 

+  19.9469 

.0050 

—  376 

—  109 

—  .  0670 

6 

—  77  57  30.lt 

.26 

1 

+  20.2912 

.0099 

—  456 

—  114 

+  .  3070 

•7 

+  32  53  28.25 

.29 

1 

+  19.8780 

.015 

—  584 

—  107 

—  .  059 

8 

+  62  14  29.68 

.21 

2 

+  19.9227 

.0057 

—  638 

—  130 

—  .0077 

9 

-j-  53  12  30.94 

.13 

5 

+  19.8621 

.0041 

—  716 

—  124 

—  .  0204 

10 

-j-  33  01  50.98 

.22 

2 

+  19.8723 

.0057 

—  C97 

—  Ill 

—  .0080 

11 

+  30  10  35.27 

.19 

3 

+  19.7476 

.  0035 

—  748 

—  Ill 

—  .1035 

12 

+  55  SI  US.  12 

.07 

20 

+  19.8006 

.0022 

—  800 

—  130 

—  .  0407 

•13 

+  65  27  41.66 

.24 

2 

+  19.  h()50 

.0111 

—  038 

—  856 

—  .  0208 

14 

—  18  40  23.23 

.07 

16 

+  19.8139 

.0033 

—  800 

—   93 

+  .  0249 

15 

+  74  18  15.68 

.12 

6 

+  19.7667 

.0048 

—  991 

—  191 

—  .  0207 

•16 

+  47  35  59.48 

.12 

6 

+  19.7748 

.0048 

—  877 

—  124 

—  .  0077 

17 

-j-  23  35  12.69 

.17 

3 

+  19.6648 

.0058 

—  900 

—  108 

—  .  0738 

18 

+  57  09  08.23 

.11 

7 

+  19.2481 

.0037 

—  1071 

—  155 

—  .  4775 

•19 

+  50  17  09.  37 

.27 

1 

+  19.6957 

•  .  0070 

—  974 

—  129 

—  .  0266 

"20 

+  60  26  17.35 

.26 

1 

+  19.8186 

.0081 

—  1100 

—  149 

+  .  1604 

21 

+  60  02  21.50 

.10 

9 

+  19.5780 

.0041 

—  1191 

—  153 

—  .0163 

*22 

+  37  49  14.69 

.12 

7 

+  19.5897 

.0048 

—  1121 

—  122 

+  .  0074 

23 

+  7  12  59.93 

.07 

17 

+  19.4721 

.0035 

—  1188 

—  101 

+  .  0233 

•24 

+  67  06  43.88 

+  19.3167 

—  1655 

—  205 

+  .  002 

25 

+  34  57  26.09 

".'io' 

10 

+  19.1852 

.0034 

—  1406 

—  125 

—  .  1223 

«26 

-f-  30  45  33.94 

.33 

1 

+  19.2696 

.0124 

—  1411 

—  119 

—  .0024 

27 

+  26  36  22.53 

.16 

3 

+  19.0389 

.0054 

—  1574 

—  117 

—  .0175 

28 

+  88  38  33.  86 

.03 

93 

+  19.0458 

.0010 

—  9670 

—11308 

+  .  0004 

•29 

+  28  05  03.38 

.24 

1 

+  18.9158 

.0060 

—  1613 

—  119 

—  .  0961 

30 

+  59  35  04.92 

.13 

5 

+  18.t:594 

.0039 

—  1978 

—  188 

—  .  0546 

31 

—  8  49  44.34 

.07 

17 

+  18.6!'02 

.0033 

—  1534 

—   90 

—  .2203 

•32 

+  69  37  12.89 

.17 

3 

+  18.7100 

.  0057 

—  2318 

—  261 

—  .  0756 

33 

—  43  57  32.  48 

.30 

1 

+  18.5496 

.0105 

—  1427 

—   60 

+  .  1342 

34 

+  14  42  02.65 

.08 

16 

+  18.6898 

.  0035 

—  1768 

—  107 

—  .  0074 

*35 

+  48  05  00.32 

.36 

1 

+  18.5480 

.0098 

—  2083 

—  155 

—  .0190 

•36 

+  47  59  38.47 

.11 

7 

+  18.3978 

.0036 

—  2125 

—  156 

—  .1189 

37 

—  57  52  20.  30 

.22 

2 

+  18.3763 

.OOH6 

—  1375 

—   40 

—  .  0474 

"38 

+  CO  03  28.61 

.10 

9 

+  18.2954 

.0040 

—  2282 

—  164 

—  .  0309 

39 

+  8  31  39.81 

.09 

12 

+  18.2459 

.  00:i7 

—  2009 

—  102 

+  .  0263 

•40 

+  50  10  25.57 

.33 

1 

+  17.9714 

.0068 

—  2496 

—  168 

—  .0449 

41 

+  63  03  11.63 

.11 

8 

+  17.9450 

.0034 

—  2828 

—  234 

—  .0247 

42 

+  28  58  08.  16 

.20 

2 

+  17.7131 

.0058 

—  2291 

—  125 

—  .2357 

43 

+  20  11  45.94 

.07 

19 

+  17.7609 

.0035 

—  2262 

—  113 

—  .1180 

44 

+  71  48  53.84 

.10 

10 

+  17.6975 

.  0036 

—  3503 

—  357 

+  .  0235 

•45 

+  63  47  06.78 

.32 

1 

+  17.6469 

.0079 

—  3108 

—  248 

+  .  0135 

N  B 38 


594          UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION.  [188J 

Catalogue  of  500  stnrx 


Number. 

i 

P 

dj 
-4 

«' 

Name. 

Magnitude. 

Approximate 
right  ascen- 
sion, 1875.0. 

a 
Id 

".2 

"3  a 
c  o 

ota 

<! 

<?% 
di* 

A.I 

iff 

46 

628 

3 

7i.  m.    s, 
1  56  13.9 

s. 
+  3.652 

s. 
+    39 

// 

+  .34 

+  .46 

47 

648 

2 

2  00  07.  8 

+  3.368 

+    21 

—  .35 

—  .75 

"48 

656 

4 

02  06.  7 

+  3.550 

+    30 

—  .32 

—  .16 

49 

684 

f  i   Ceti             

5 

06  22.5 

+  3.  170 

+     14 

—  .20 

—  .43 

"50 

744 

4 

18  47.  5 

+  4.844 

+  131 

—  .03 

+  .77 

"51 

752 

6.5 

20  03.8 

+  3.535 

+    27 

—  .42 

+  .07 

52 

760 

fi  Ceti          

4 

21  30.9 

+  3.  181 

+     I'-J 

—  .16 

+  .28 

53 

777 

5.5 

26  11.4 

+  5.553 

+  200 

+  .36 

+1.57 

•54 

825 

6 

35  19.3 

+  3.370 

+    18 

—  .26 

—  .22 

55 

827 

9    Persei       

4 

35  40.2 

+  4.061 

+    51 

+1.14 

+  1.29 

56 

837 

•yi  Ceti          

3 

36  49.  5 

+  3.  103 

+      9 

—  .56 

—  .45 

57 

863 

4 

41  35.5 

+  4.333 

+    68 

+  .66 

+3.10 

58 

872 

3 

42  37.  8 

+  3.514 

+    23 

-.69 

+  .15 

59 

885 

5 

45  24.  3 

+  4.212 

+    58 

—  .08 

+  .46 

"GO 

896 

6 

49  33.  8 

+  7.668 

+  457 

+  .55 

-1-2.  19 

61 

937 

gi    Eridani      

3.5 

53  31.2 

+  2.  274 

+      7 

—  .43 

—1.35 

62 

949 

a    Ceti          

2.5 

55  44.8 

+  3.  129 

+  10 

—  .17 

+  .21 

63 

947 

3.5 

55  45.  3 

+  4.307 

+    59 

+  .49 

+1.17 

64 

953 

4 

57  10.3 

+  3.  821 

+    33 

—  .41 

—  1.  27 

65 

963 

2.5 

3  00  02.  4 

+  3.878 

+    35 

—  .07 

—1.62 

60 

962 

4 

00  03.3 

+  4.294 

+    52 

+  .23 

—1.18 

"67 

979 

5.5 

04  32.  1 

+  7.360 

+  353 

+  .48 

+1.41 

"68 

999 

5 

07  43.  1 

+  3.436 

+    18 

—  .23 

—  .  32 

*69 

1029 

7 

13  01.2 

+  3.542 

+    20 

—  .24 

+  .34 

70 

1043 

2.5 

15  24.  4 

+  4.249 

+    48 

—  .04 

+  .56 

71 

1057 

4.5 

18  05.  3 

+  3.221 

+     11 

—  .22 

—  .55 

72 

106-i 

f    Tauri            .     

4 

20  23.8 

+  3.244 

+    12 

+1.  52 

+  .77 

•73 

1067 

6 

21  33.  3 

+  6.430 

+  204 

+  .68 

+2.78 

*74 

1101 

6.5 

27  51.4 

+  3.708 

+    24 

+  .12 

+  .90 

75 

1129 

(J    Persei  ...  .  

3 

34  01.8 

+  4.241 

+    41 

-.30 

-.08 

*76 

1127 

6 

34  12.7 

+  5.600 

+  116 

—  .13 

+  .30 

77 

1166 

ij    Tauri    

3 

40  03.  4 

+  3.555 

+    13 

—  .37 

—  .78 

78 

1207 

f    Persei 

3  5 

46  16  6 

+  3  757 

I    22 

—  .29 

—  .73 

*79 

1203 

5 

46  24.7 

+  5.242 

+    84 

—  .21 

—  .26 

*80 

1228 

5 

50  51.5 

+  3.873 

+    25 

—  .84 

—  .71 

81 

1234 

yl   Eridani  

2.5 

52  11.8 

+  2.794 

+      4 

—  .34 

+  .40 

*82 

1254 

7i    Persei  

4.5 

57  16.7 

+  4.440 

+    42 

—  .15 

—  .37 

83 

1235 

c 

57  58.1 

+16.  853 

+1811 

+  .86 

+3.  28 

84 

1266 

48  Persei   

5 

59  35.5 

+  4.331 

+    37 

—  .87 

-  .90 

"85 

1287 

fjt    Persei  

4.5 

4  05  43.  5 

+  4.380 

+    37 

+  .13 

+  .58 

P6 

1328 

3.5 

12  40  9 

+  3.408 

+     11 

—  .88 

—2.55 

87 

1376 

e    Tauri  

3.5 

21  19.  1 

+  3.496 

+     12 

—  .13 

—1.  67 

88 

1420 

a    Tanri 

1 

28  45  0 

-\-  3.436 

+   10 

—  .25 

—  l.Orf 

89 

1456 

4     Canaelopardi 

5 

37  35  9 

+  4.9C9 

+    40 

+  .28 

+  .00 

90 

1474 

a    Camelopardi 

4 

41  38,0 

+  5  915 

+    69 

—  .24 

—2.  14 

[189] 


CATALOGUE  OF  500  STARS. 


595 


for  the  epoch  1875.0 — Continued. 


Number. 

Declination,  1875.0. 

Probable  error 
of  f,  1875. 

S 

M 

1 

Annual  varia- 
tion, 1875.0. 

Probable  error 
of  nnnual  va- 
riation. 

<P<5 
M' 

a?s 

di3 

1 

o 

e-o' 

-  n 

IT 

2 

PH 

o   /    // 

II 

// 

ti 

it 

II 

// 

46 

+  41  43  43.50 

.13 

5 

+  17.4676 

.0036 

—  2663 

—  149 

—  .0624 

47 

+  22  52  13.  17 

.06 

25 

-f  17.2103 

.  C021 

—  2543 

—  116 

—  .1515 

*48 

+  34  23  41.73 

.11 

7 

4-  17.2248 

.0037 

—  2714 

—  136 

—  .0496 

49 

+  8  15  3:*.  55 

.11 

8 

4-  17.0666 

.0040 

—  2492 

—   97 

—  .0153 

•50 

+  66  50  19.27 

.11 

7 

4-  16.4926 

.  0043 

—  4097 

—  310 

+  .  0047 

*5l 

+  31  14  19.64 

.25 

1 

+  16.3870 

.0075 

—  3031 

—  129 

—  .  0373 

53 

4-  7  53  55.03 

.08 

14 

+  16.3369 

.0036 

—  2758 

-   95 

—  .014: 

53 

+  72  16  09.56 

.19 

3 

4-  16.1156 

.0063 

—  4883 

—  432 

+  .  0047 

•54 

+  19  28  38.91 

.22 

2 

4-  15.5662 

.C073 

—  3148 

—  107 

—  .0513 

55 

+  48  41  53.24 

.20 

2 

4-  15.5050 

.0051 

—  3819 

—  181 

—  .0981 

56 

+  2  42  28.16 

.08 

16 

+  15.3820 

.0029 

—  2919 

—   85 

—  .1575 

57 

+  55  22  29.46 

.23 

2 

+  15.2466 

.0065 

—  4166 

—  213 

—  .  0260 

58 

+  26  44  37.79 

.11 

7 

+  15.0941 

.0042 

—  3407 

—  118 

—  .  1195 

59 

-i-  52  14  56.  91 

.13 

5 

4-  15.0427 

.0048 

—  4122 

—  194 

—  .0114 

•60 

+  78  55  16.59 

.16 

4 

+  14.8183 

.0053 

—  7610 

—  904 

-f  .  OU69 

61 

—  40  48  22.  63 

.29 

1 

+  14.6222 

.0101 

—  2336 

—   45 

+  .  0465 

62 

+  3  35  52.89 

.06 

22 

-j-  14.3553 

.  0023 

—  3226 

—  '  82 

—  .  0859 

63 

+  53  00  54.  54 

.23 

2 

4-  14.4384 

.0068 

—  4424 

-  198 

—  .0023 

64 

+  38  21  15.39 

.20 

2 

4  14.2417 

.0061 

—  3963 

—  141 

—  .1127 

65 

+  40  28  20.48 

.09 

19 

4-  14.1657 

.0029 

—  4058 

—  146 

—  .  0122 

66 

+  49  08  01.33 

.21 

2 

+  14.0-53 

.0061 

—  4631 

—  193 

—  .0918 

*67 

-f  77  16  19.  19 

.11 

7 

+  13.8452 

.  0031 

—  7819 

—  763 

—  .  0519 

*68 

+  20  34  46.86 

.11 

7 

4  13.6107 

.  0042 

—  3716 

—  101 

—  .  Ori42 

"69 

+  25  12  38.65 

.24 

2 

4  13.2529 

.0089 

—  3912 

—  107 

—  .0996 

70 

+  49  24  51.43 

.08 

13 

4  13.  1625 

.0030 

—  4725 

-  175 

—  .0334 

71 

+  8  35  14.68 

.14 

5 

+  12.9299 

.0048 

—  3624 

—   81 

—  .  0885 

72 

+  9  17  43.17 

.12 

6 

4  12.r077 

.0044 

—  3688 

—   82 

—  .0563 

*73 

+  72  55  12.89 

.29 

1 

+  12.7748 

.0121 

—  7273 

—  502 

—  .0112 

•74 

+  31  15  38.51 

.27 

1 

4-  12.3255 

.015 

—  4316 

—  114 

—  .031 

75 

4-  47  23  08.49 

.08 

13 

4  11.8o28 

.0029 

—  5024 

—  158 

—  .0438 

•76 

-f  66  48  24.09 

.21 

2 

+  11.8228 

.0079 

—  6642 

—  329 

—  .0910 

77 

+  23  43  00.57 

.07 

18 

+  11.4429 

.  0029 

—  4298 

—   94 

—  .0558 

78 

+  31  30  37.56 

.09 

11 

4  11.0171 

.  0036 

—  4621 

—  106 

—  .0313 

•79 

4-  62  42  10.78 

^26 

1 

+  11.0480 

.0094 

—  6422 

—  257 

+  .  0094 

•80 

+  35  25  46.51 

.20 

2 

4-  10.6936 

.0056 

—  4825 

—  112 

—  .0181 

81 

—  13  51  F.6.04 

.08 

16 

+  10.4965 

.0033 

—  3507 

—   46 

—  .1100 

"82 

+  50  00  34.57 

.12 

6 

4-  10.  1890 

.  0043 

—  5617 

—  154 

—  .  0437 

83 

+  85  13  20.27 

.19 

3 

4-  10.2135 

.0066 

—21219 

—  37S6 

-f  .  0328 

84 

+  47  22  34.67 

.23 

2 

4-  10.0150 

.0060 

—  5510 

—  142 

—  .  0430 

;  "as 

+  48  05  21.69 

.22 

2 

+  9.5579 

.  0057 

—  5652 

—  139 

—  .  0322 

86 

+  15  19  26.23 

.09 

11 

4  9.  0238 

.0040 

—  4486 

—   67 

—  .  0275 

67 

+  18  54  04.44 

.08 

16 

4  8.  3258 

.  0039 

—  4679 

—   66 

—  .0447 

88 

+  16  15  21.78 

.06 

26 

+  7.5K5H 

.0021 

—  4658 

-   58 

—  .1918 

89 

+  56  31  56.  13 

.11 

7 

4  6.  9050 

.  0042 

—  6819 

—  141 

—  .1510 

90 

4-  66  07  36.73 

.10 

.  8 

-f  6.  7231 

.0037 

—  8151 

—  213 

—  .  0014 

596          UNITED  STATES  NORTHERN    BOUNDARY  COMMISSION.         [LJK)J 

Catalogue  of  500  stars 


Number. 

a 

3 
a 

tig 
<i 
» 

Name. 

Magnitude. 

Approximate 
right  asceu- 
sion,  1875.0. 

i 

Id 

>a 

"3  o 
s  o 
a'S 
a 
<! 

<i»a 
dt? 

i(! 

AX 

91 

1520 

4 

h.  m.     s. 
4  48  51.3 

8. 

4-  3.897 

II 

+     14 

a 

—  .81 

// 
—  .95 

92 

1536 

4.5 

52  18.3 

+  5.309 

+     42 

4-  .12 

—  .34 

93 

1540 

4 

53  00.0 

+  4.292 

+     '-0 

—  .23 

—  1.29 

94 

1541 

4 

53  44.5 

+  4.  181 

+     1s 

4-  .31 

+  .48 

95 

1557 

5 

57  25.7 

+  3.425 

+       s 

—  1.07 

—2.75 

96 

1558 

4 

57  45.  1 

4-  4.  196 

+     17 

—  .23 

—1.18 

97 

1613 

1 

5  07  27.4 

4-  4.422 

4-     16 

—  .  16 

—  .74 

98 

1023 

1 

08  31.9 

4-  2.881 

+      4 

4-  .10 

—  .  11 

99 

1681 

0    Tauri                  

2 

18  23.5 

4-  3.788 

-L      8 

—  .36 

—  .47 

100 

1706 

5 

23  01.6 

+  7.990 

+     77 

+  .83 

4-2.11 

101 

1730 

2 

25  37.3 

4-  3.0<i4 

+      4 

4-  .09 

4-2.00 

102 

1741 

3.5 

27  13.1 

+  2.645 

+       3 

—  .36 

—  .06 

103 

1765 

2.5 

29  52.  3 

+  3.042 

+       4 

—  .46 

—  .36 

104 

1802 

2 

35  07.  4 

+  2.  173 

+       3 

—  .62 

—  .51 

105 

1845 

5 

42  49.6 

+  4.  155 

+      6 

4-  .10 

—  .31 

106 

1878 

3 

46  33.2 

+  2.113 

+      :? 

—  .12 

—  .  11 

107 

1883 

1 

48  24.3 

-f  3.247 

4-      3 

—  .01 

—  .02 

108 

Ie85 

3.5 

49  14.  1 

4-  4.  9:i6 

+      6 

—  .02 

—  .52 

109 

1895 

2 

50  21.5 

4-  4.395 

+      4 

—  .14 

.25 

110 

1900 

4 

51  11.8 

4-  4.090 

+      3 

4-  .22 

4-2  30 

111 

1980 

5 

6  05  03.  9 

+  6.  61'J 

—       7 

—  .40 

—1.13 

112 

2002 

4 

07  20.  0 

+  3.622 

4-      1 

4-  .08 

4-  .19 

113 

2047 

3 

15  23  9 

4-  3  633 

1 

86 

1  46 

114 

2096 

1 

21  10.5 

+  1.330 

4-      1 

—  .13 

4-  .87 

115 

2163 

2.5 

30  29.4 

4-  3.469 

±      1 

—  .25 

—1.36 

116 

2194 

3 

36  14  5 

4-  3.694 

_       3 

4-  .23 

—  .12 

117 

2157 

5 

41  14.7 

+30.  234 

—2101 

+  .03 

—  .11 

118 

2237 

5 

44  32  9 

4-  3  960 

_      7 

—  .29 

—1.02 

119 

2293 

2  5 

53  42  8 

4-  2  357 

4-      2 

—  .43 

4-  .72 

120 

2303 

4 

56  41.7 

4-  3.563 

—      5 

4-  .37 

—1.14 

121 

2345 

<5    Can's  Majoris. 

3  5 

7  03  18  5 

4-  2  439 

4.       l 

—  .81 

4-  .93 

122 

2398 

/I    Gemiuorum     ... 

4.5 

10  54.5 

4-  3  453 

—      5 

4-  .62 

—  .99 

123 

2410 

6    Gemiuorum 

3 

12  39  4 

-f-  3  591 

_      7 

—    96 

2.53 

124 

2439 

5 

17  51  4 

+  0  311 

—    84 

4-1.38 

4-3.  55 

125 

2442 

i     GemiDoruiu.  .    

4 

17  57  7 

-)-  3  736 

—     10 

—  .08 

—  .08 

126 

2462 

3 

20  22  3 

+  3  257 

—      4 

—  .13 

—  .58 

127 

2485 

c2  Geininorum  

1.5 

26  37  0 

+  3  839 

—     13 

4-  .03 

—  .  13 

128 

2551 

K    Geminorum         

4 

36  54  0 

4-  3  629 

—     11 

4-  .57 

—1.13 

129 

2555 

/3    Geminorum  .  .  

2 

37  39  9 

4-  3  681 

—     13 

—  .33 

—  .35 

130 

2617 

0    Geminorum  .  

5 

45  50  8 

4-  3  684 

—     13 

—  .33 

—1.06 

131 

2710 

£     Argus  .  .  

2.5 

59  11  5 

4-  2  lOd 

4-       1 

4-  .08 

—  .03 

132 

2707 

55  Camclopardi  .  

5 

8  00  20  9 

4-  6  066 

—  119 

4-  .57 

4-1.30 

133 

2728 

p    Argus  

3.5 

02  13.3 

+  2  554 

+      1 

—  .51 

—1.46 

134 

2778 

P    Cancri  

4 

09  44.  1 

+  3  257 

—  .27 

—  .10 

135 

2819 

o    Ursse  Majoris 

4 

19  51  9 

4-  5  043 

76 

4-     22 

4-    34 

[191]  CATALOGUE  OF  500  STABS. 

for  the  epoch  1875.0 — Continue  J. 


597 


Number. 

Declination,  1875.0. 

Probable  en-or 
of  i,  1875. 

| 

C 

fe 

«  . 

1§ 

>  i  - 

00 

"3  "1 
g§ 

3* 

Probable  error 
of  anunal  va- 
riation. 

<P<5 
dp 

tPi 
dt3 

a 
_o 
9 
o 
S-c 

>.  = 
<o  •" 
& 

1 

o   /    // 

a 

ir 

a 

it 

a 

// 

91 

+  32  57  57.28 

.08 

15 

+  6.  1044 

.0033 

—  5437 

—   65 

-  .  0215 

92 

-j-  60  15  22.90 

.11 

8 

+  5.  8243 

.0041 

—  7431 

—  139 

—  .0134 

93 

+  43  3d  09.00 

.11 

8 

+  5.  7606 

.0031 

—  6017 

—   79 

—  .  0169 

94 

+  40  53  27.31 

.20 

2 

+  5.  6922 

.  0051 

—  5868 

—   72 

—  .0252 

95 

-f  15  13  40.70 

.12 

7 

+  5.3fc90 

.0044 

—  4837 

—   40 

—  .0385 

96 

+  41  C3  46.64 

.11 

7 

+  5.3065 

.0033 

—  5921 

—   69 

—  .0738 

97 

+  45  52  05.56 

.06 

23 

-f  4.  1231 

.0020 

—  6312 

—   64 

—  .4344 

98 

—  8  20  51.96 

.06 

24 

+  4.  4598 

.0022 

—  4114 

—   22 

—  .0061 

99 

+  28  29  58.49 

.06 

25 

+  3.  4402 

.C021 

—  5452 

—   34 

—  .1807 

100 

-j-  74  57  22.41 

.16 

4 

-f  3.  2404 

.0061 

—11526 

—  210 

+  .  0191 

101 

—  0  23  36.71 

.07 

16 

+  2.9920 

.0029 

—  4433 

—   17 

—  .0050 

102 

—  17  54  48.06 

.09 

10 

+  2.8581 

.0038 

—  3832 

—   11 

—  .0006 

103 

—  1  17  00.94 

.08 

15 

+  2.6292 

.0033 

—  4409 

—   14 

+  .  0004 

104 

—  34   8  31.22 

.16 

4 

+  2.1273 

.'•066 

—  3163 

—   7 

—  .  0451 

105 

+  39  06  33.53 

.21 

2 

+  1.  5192 

.0060 

—  6047 

—   17 

+  .0179 

106 

—  35  48  59.72 

.27 

1 

+  1.  5648 

.0086 

—  3087 

—   5 

+  .3889 

107 

-f  7  22  54.34 

.06 

26 

+  1.  0210 

.0021 

—  4735 

—   5 

-f-  .0068 

108 

+  54  16  19.12 

.11 

7 

+  0.8114 

.0044 

—  7206 

—   14 

—  .  1302 

109 

-j-  44  55  55.62 

.09 

12 

+  0.  8399 

.0028 

—  6392 

—   10 

—  .  0035 

110 

+  37  12  04.  92 

.17 

3 

+  0.  6751 

.0060 

—  5968 

—   6 

—  .0950 

111 

+  69  21  35.  08 

.13 

5 

—  0.5615 

.0055 

—  9645 

+   28 

—  .1183 

112 

-f  22  32  27.  18 

.10 

10 

—  0.  6576 

.0041 

—  5270 

+    8 

—  .0161 

113 

+  22  34  31.  93 

.08 

16 

—  1.  4680 

.0030 

—  5289 

+   15 

—  .1216 

114 

—  52  37  40.  83 

.23 

2 

—  1.8416 

.0085 

—  1925 

+   2 

+  .  0087 

115 

+  16  30  14.10 

.07 

19 

—  2.  7078 

.  0033 

—  5009 

+   23 

—  .  0476 

116 

-)-  25  15  09.76 

.14 

4 

-  3.1732 

.0051 

—  5306 

+   32 

—  .0152 

117 

+  87  14  04.  35 

.07 

19 

—  3.6289 

.0033 

—43^67 

+  4794 

—  .0391 

118 

+  34  06  34.48 

,11 

8 

—  3.  9229 

.0047 

—  5648 

+   48 

—  .0492 

119 

—  28  48  12.  13 

.11 

7 

—  .  4.6700 

.0059 

—  3324 

+   14 

—  .0128 

120 

-f  20  45  05.75 

.11 

8 

—  4.9219 

.0040 

—  5017 

+   44 

—  .0114 

121 

—  26  11  45.81 

.12 

6 

—  5.4602 

.0055 

—  3393 

+   1« 

-f  .  0093 

122 

+  16  45  50.12 

.16 

4 

—  6.1521 

.0047 

—  4767 

+   50 

—  .0459 

123 

+  22  12  37.60 

.07 

18 

—  6.  2680 

.0029 

—  4948 

+   57 

—  .0163 

124 

+  68  43  03.  10 

.16 

4 

—  6.7199 

.0058 

—  8652 

-f.  264 

—  .0375 

125 

+  28  02  39.96 

.14 

4 

—  6.7729 

.0048 

—  5097 

+   68 

—  .0818 

126 

+  8  32  21.67 

.10 

10 

—  6.9393 

.0041 

—  4426 

+   48 

—  .0498 

127 

+  32  09  37.90 

.07 

19 

—  7.4784 

.0024 

—  5152 

+   80 

—  .  0783 

128 

+  24  41  44.66 

.15 

4 

—  8.  2919 

.0051 

—  4787 

+   76 

—  .0633 

129 

-f  28  19  34.20 

.06 

26 

—  8.3472 

.0020 

—  4790 

•  +   79 

—  .0575 

130 

+  27  05  14.74 

.11 

8 

—  8.  9607 

.0041 

—  4771 

+   85 

—  .0246 

131 

—  39  39  06.72 

.30 

1 

—  9.9360 

.0096 

—  2621 

+   24 

+  .0297 

132 

+  68  50  20.20 

.14 

4 

—  10.0515 

.0053 

—  7619 

-f  353 

-f  .  0020 

133 

—  23  56  42.  71 

.10 

9 

—  10.1495 

.0043 

—  3155 

+   37 

-f  .  0454 

134 

+  9  34  09.08 

.09 

10 

—  10.  8076 

.0039 

—  3956 

+   73 

—  .0520 

135 

+  61  08  00.80 

.12 

6 

—  11.  6155 

.0037 

—  5957 

+  251 

—  .1226 

598 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[192] 


Catalogue  of  500  stars 


Number. 

S 

s 

dj 

<i 
«' 

Name. 

Magnitude. 

Approximate 
right  ascen- 
sion, 1875.0. 

Anuual  varia- 
tion in  a. 

(Pa 

at' 

J.r! 

V 

136 

137 
138 
139 
140 

141 
142 
143 
144 
145 

146 

147 
148 
149 
150 

151 

152 
153 
154 
155 

156 
157 
158 
159 
160 

161 
162 
163 
164 
165 

166 
167 
168 
169 
170 

171 

172 
173 
174 
175 

176 
177 

178 
179 
180 

2953 
2965 
2971 
304^ 
3075 

3099 
3111 
3126 
3178 
3186 

3199 
3223 
3232 
3242 
3312 

3331 
3346 
3371 
3453 
3459 

3496 
3505 
3523 
3533 
3593 

3609 
3695 
3708 
3767 
3777 

3812 
3834 
383-i 
3852 
3859 

3900 
3914 
3946 
3981 
3995 

4002 
4017 
4072 
4112 
4123 

6    Cancri       .    ......  

4.5 
5 
4 
3.5 
4 

5 
5 
3 

4 
2 

5 
2 
5 
3 

4 

3 
4 
3 
3.5 
1 

5 
3.5 
2 
3 
5.5 

4 
2 
6 
2 
1.5 

3.5 
2.5 
3 
4 
3.5 

4 
3.5 
4.5 

4 
2.5 

3.5 
2 
4.5 
5 
3 

h.  »i.     s. 
8  37  34.  8 
39  07.  8 
40  09.  4 
50  38.4 
55  05.  0 

59  22.  0 
9  00  58.5 
03  23.  9 
13  26.  1 
13  44.  6 

19  05.9 
21  26.7 
23  23.  5 
24  29.  1 
34  28.6 

38  45.  2 
42  05.  1 
45  39.  0 
10  00  31.0 
01  42.8 

08  56.  0 
09  33.  1 
13  04.  7 
14  £2.6 
24  25.  0 

2fi  13.7 
40  12.9 
42  41.1 
54  17.3 
55  59.8 

11  02  37.7 
07  27.5 
07  40.8 
11  43.4 
'  13  05.  5 

21  30.5 
23  57.5 
30  32.  9 
39  26.7 
42  41.0 

44  11.0 
47  14.8 
58  50.  5 
12  06  19.  4 
09  13.9 

+  3.419 
+  3.  644 
+  3.184 
+  4.  1:59 
+  4.  125 

+  5.374 
+  3.255 
4-  2.  202 
4-  3.672 
+  1.606 

+  9.  113 
+  2.949 
+  5.425 
+  4.050 
+  3.207 

+  3.419 
+  4.  330 
+  3.424 
+  3.278 
+  3.202 

+  4.  437 
+  3.646 
+  3.  317 
+  3.602 
+  5.303 

+  3.  166 
4-  2.310 
4-  3.159 
+  3.367 
+  3.758 

+  3.  398 
+  3.202 
+  3.  155 
+  3.258 
+  2.995 

—  3.  088 
+  3.637 
+  3.  072 
-(-  3.  197 
+  3.  065 

+  3.  125 
+  3.188 
+  3.058 
+  2.904 
4-  3.003 

s. 
—    13 
—    20 
—      7 
—    44 
—     44 

—  134 

—      9 
+      4 
—    27 
o 

—  795 
—      2 
—  169 
—    55 
—      9 

—    18 
—    82 
—    20 
—    13 
—     10 

—  115 
—    38 
—     15 
—    36 
—  280 

—      8 
+    22 
—      8 
—    63 
—    81 

—    37 
—    13 
—    10 
—    23 
+      6 

—      2 
—  Ill 
0 

—    36 

—      7 

0 

—    44 
3 

—  126 
—    43 

// 

+  .00 
—  .22 
—1.17 

—  .20 
+  .91 

+1.95 

—  .87 
—  .04 
—  .08 
+  .22 

—1.  06 
—  .03 
—  .32 
—  .13 

+  .38 

—  .43 
+  .17 
—  .54 
—  .56 
—  .32 

+  .61 
—  .27 
—1.  24 
—  .18 
—  .51 

—  .54 
—  .06 
—1.10 
—  .64 
+  .01) 

—  .27 
—  .54 
+  .34 
—  .01 
—  .53 

—  .57 
+1.59 
—  .86 
13 

// 

—  .18 
—1.15 
—3.17 
+  .02 
+2.79 

+3.  92 
—2.47 
—1.74 

—  .18 
+2.82 

—2.34 

—  .48 
—  .01 
+  .85 
—  .03 

—1.46 
—  .42 

—  .6(5 
—1.84 
1  30 

i     Caucri          ....  

K    Ursge  Majoris  .  

>t    Argus..       .  . 

i     Argus  ......  

a    Hydras  ... 

24  Ureas  Majoris  .   ... 

Q    Ursai  M;t  joris      ...... 

e    Leouis        -         .  .... 

v    Ursae  Majoris 

jt    Leouis  . 

ri    Leonis 

a     Leonis                  . 

32  Ureoe  Majoris  

+  .95 
+  .41 
—2.65 
—1.36 
—1.11 

—  .98 
—  .38 
—2.78 
—2.  70 
+  .04 

—  .18 
—2.34 
—1.22 
—1.28 
+  .35 

—1.20 
+3.84 
-    l.fc'O 
—  .52 
—2.51 

—1.05 
—  .05 
—1.22 
+2.  <J3 
+  .92 

A    Ursa?  Majoris  

y1   Ursai  Majoris  .... 

p    Leonis  

ft    Argus  

53  Leonis  

/3    Ureae  Majoris  

a    Ursse  Majoris  .  

ip    UrssB  Majoris  ....   .. 

fi    Leonis  .  .  .. 

6    Leonis  ..  .  

v    Ursse  Majoris  .  .  

<i    Crateris  

r    Leon's  

A    Draconis  

v     Leonis  

X    Ursse  Majoris  

J3    Leonis  

—  .47 

—  .43 
+  .28 
—  .76 
+1.67 
+  .06 

/?    Virginis   

y    Ursee  Majoris  

o    Virginis  

&    Ursaj  Majoris  

[193] 


CATALOGUE  OF  500  STARS. 


599 


for  the  epoch  1875.0 — Continued. 


Number. 

Declination,  1875.0. 

Probable  error 
of  6,  1875. 

1 
1 

c3  . 
'CO 
m<6 

P6 

>—  <  i—  t 

a  - 
3  g 

o  2 
p  — 
«! 

Probable  error 
of  annual  va- 
riation. 

cPi 
dl* 

(P6 
di:> 

Proper  motion 
in  <S. 

O    /     It 

n 

// 

it 

II 

II 

// 

13C 

+  18  36  44.17 

.12 

6 

—  12.9634 

.  0039 

—  3797 

+   9(5 

—  .  2358 

137 

4-  29  12  55.56 

.20 

2 

—  12.8937 

.0060 

—  4025 

4-  115 

—  .C015 

138 

-j-  6  52  34.59 

.07 

17 

—  12.9548 

.0030 

—  3486 

4-   80 

—  .  0537 

139 

4-  48  31  50.  87 

.08 

15 

—  13.8425 

.0020 

—  4333 

+  173 

—  .2528 

140 

4-  47  38  57.05 

.17 

3 

—  13.9401 

.0047 

—  4279 

+  174 

—  .0671 

141 

+  67  38  23.  33 

.12 

6 

—  14.  1971 

.0041 

—  5494 

+  359 

—  .0558 

14-2 

4-  11  10  11.92 

.08 

14 

—  14.2444 

.0040 

—  3278 

+   92 

—  .  0037 

143 

—  42  55  43.  04 

.30 

1 

—  14.3765 

.0102 

—  2171 

+   34 

+  .  0126 

144 

+  34  55  11.02 

.10 

9 

—  14.9717 

.  0039 

—  3474 

+  135 

+  .0152 

145 

—  58  45  03.78 

.25 

1 

—  14.9766 

.0098 

—  I486 

+   24 

+  .0282 

146 

+  81  52  32.83 

.12 

7 

—  15.3300 

.0046 

—  8510 

4-  1423 

—  .0184 

147 

—  8  07  04.31 

.07 

22 

—  15.4132 

.0023 

—  2li7<) 

+   75 

+  .  0302 

148 

+  70  22  40.25 

.18 

3 

—  15.4916 

.  00(;1 

—  4915 

-j-  401 

+  .  0599 

149 

-f-  52  14  44.25 

.08 

13 

—  16.  1682 

.0028 

—  3548 

+  185 

—  .  5565 

150 

+  10  27  35.91 

.10 

8 

—  16.1769 

.0037 

—  2094 

4-   98 

—  .  0333 

151 

+  24  20  55.41 

.07 

19 

—  16.3863 

.0080 

—  2810 

-f  119 

—  .0216 

15d 

4-  59  37  31.  17 

.11 

8 

—  16.6917 

.0033 

—  3476 

+  2.i3 

—  .  1602 

153 

+  26  35  40.61 

.08 

13 

—  16.7587 

.0034 

—  2676 

+  121 

—  .  0526 

154 

+  17  22  16.68 

.18 

3 

—  17.3984 

.  0053 

—  2304 

+  110 

—  .  0084 

155 

+  12  34  38.26 

.06 

27 

—  17.4430 

.0020 

—  2217 

+  10,i 

—  .0010 

156 

+  65  43  50.60 

.14 

5 

—  17.7705 

.0060 

—  2927 

4-  265 

—  .0255 

157 

4-  43  32  15.64 

.10 

9 

—  17.  8131 

.0032 

—  2378 

+  152 

—  .0429 

153 

4-  20  28  22.85 

.07 

19 

—  18.0565 

.  0028 

—  2112 

4-  117 

—  .  1455 

159 

4-  42  07  38.22 

.12 

C 

—  17.9619 

.0040 

—  2245 

4-  148 

4-  .  0194 

160 

+  76  21  20.  73 

.11 

7 

—  18.3514 

.0044 

—  3054 

4-  441 

—  .0161 

161 

+  9  56  56.87 

.08 

14 

—  18.4077 

.0035 

—  1758 

4-  101 

-  .0088 

164 

—  59  01  39.76 

.22 

2 

—  18.8551 

.0088 

—  1067 

4-   43 

—  .0038 

163 

+  11  12  21.88 

.08 

13 

—  18.9527 

.0043 

—  1443 

4-  105 

—  .0288 

164 

+  57  03  06.52 

.09 

11 

—  19.2275 

.0036 

—  1435 

+  165 

4-  .  ooeo 

165 

+  62  25  31.31 

.06 

24 

—  19.3439 

.0021 

—  1420 

+  177 

—  .0666 

166 

+  45  10  34.53 

.09 

12 

—  19.4710 

.0031 

—  1141 

+  133 

—  .0418 

167 

+  21  12  29.60 

.07 

21 

—  19.6719 

.0026 

—  981 

H-  112 

—  .1424 

168 

-j-  16  06  45.03 

.18 

3 

—  19.6111 

.0055 

—  956 

+  107 

—  .0772 

169 

+  33  46  33.99 

.24 

2 

—  19.5798 

.0062 

—  909 

+  118 

+  .  0312 

170 

—  14  06  08.73 

.08 

15 

—  19.4521 

.0034 

—  801 

+   92 

+  .1835 

171 

+  3  32  39.95 

.10 

9 

—  19.7930 

.0039 

—  668 

+  101 

—  .0210 

172 

4-  70  01  14/63 

.09 

12 

—  19.8274 

.0030 

—  743 

+  164 

—  .0206 

173 

—  0  08  01.73 

.08 

15 

—  19.8539 

.0035 

—  489 

+  100 

+  .  O.!50 

174 

4-  48  28  20.68 

.11 

8 

—  19.9549 

.0034 

—  330 

+  115 

4-  .0188 

175 

-j-  15  16  14.62 

.06 

25 

—  20.  1161 

.0021 

—  248 

+   99 

—  .  1191 

r/6 

4-  2  28  08.39 

.09 

12 

—  20.  2890 

.0028 

—  233 

4-  105 

—  .2825 

177 

4-  54  23  22.85 

.07 

20 

—  20.0247 

.  0022 

—  173 

+  112 

—  .0015 

178 

+  9  25  38.37 

.09 

12 

—  20.  0162 

.0036 

+   64 

+   99 

4-  .0378 

179 

+  78  18  39.34 

.10 

9 

—  20.  0253 

.0043 

+  203 

+   85 

+  .  0213 

180 

+  57  43  38.28 

.11 

8 

—  20.02*8 

.0035 

+  263 

4-   93 

4-  .  0092 

600 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[194] 


Catalogue  of  500  stars 


Number. 

3 

B 

a 
dj 
< 
« 

Name. 

Magnitude. 

Approximate 
right  asceu- 
aion,  1875.0. 

C3 

IB 

>£ 

"3  a 
a  o 

D'£ 

a 
<! 

<Fo 

3P 

Aa 

v 

181 

182 
183 
"184 
*li-5 

]86 

187 
*188 
189 
*190 

191 

*192 
193 
194 
*195 

196 
197 
*198 
•199 
200 

*201 
"202 
203 
204 

*205 

206 
*207 
208 
»209 
210 

211 

•212 
213 
214 
215 

•216 
217 
218 
219 
*220 

221 

222 
223 
224 
*225 

4131 
4145 
4187 
4191 
4222 

4234 
4239 
4258 
4342 
4335 

4346 
4366 
4401 
4421 
4433 

4480 
4484 
4506 
4513 
4532 

4540 
4596 
4607 
4618 
4637 

4648 
4659 
4669 
4675 
4696 

4706 
4732 
4729 
4741 

4789 

4804 
4808 
4812 
4822 

4827 

4832 
4864 
4876 
4895 
4897 

/?    Chameleonfria.-  

5 
3.5 
1 
5 
5.5 

2.5 
3  5 

h.   m.    s. 
12  11  03.5 
13  30.  7 
19  39.5 
20  08.9 
24  37.  5 

27  49.3 
28  08.3 
32  45.  2 
48  13.8 
48  31.  5 

50  10.7 
55  21.  7 
13  03  28.  8 
06  02.3 
08  02.7 

18  36.  6 
18  53.4 
22  56.7 
24  56.6 
28  19.5 

29  18.9 
40  55.  1 
42  36.8 
43  48.  2 
47  14.6 

48  44.  0 
50  29.  3 
51  01.  1 
55  30.  4 
14  01  00.4 

04  42.0 
09  45.  0 
09  57.  6 
11  37.8 
20  56.  5 

24  16.9 
26  26.  6 
27  02.6 
27  48.8 
29  31.8 

31  07.2 
37  55.7 
39  31.7 
43  57.  9 
44  12.3 

+  3.380 
+  3.068 
+  3.282 
+  3.009 
+  2.677 

--)-  3.  132 
+  2.600 
+  2.904 
+  0.361 
+  2.661 

+  2.817 
+  2.  592 
+  3.  101 
+  2.807 
+  2.730 

+  3.  152 
+  2.  421 
+  1.518 

+  2.848 
+  3.053 

+  2.320 
+  2.555 
+  2.  374 
+  .2.840 

+  2.867 

+  2.  859 
—  0.  014 
+  4.  170 
+  2.724 
+  1.623 

+  2.739 
+  1.098 
+  2.735 
+  2.284 
+  2.  043 

+  2.  088 
-j-  2.  587 
+  2.  418 
—  0.  208 
+  2.  186 

+  4.029 
+  2.639 
+  2.621 
+  3.309 
+  2.357 

8. 

+  180 
+      3 
+    08 
—    12 

—    58 

+    l(i 
—    54 
—    19 
+  221 
—  273 

—    15 
—    25 
+      8 
—      8 
—    14 

+     H 
—     17 

±      I 
+      6 

—     14 

—      9 
—    10 
—      2 
—      6 

0 
+  182 
+    84 
—      3 
+      5 

—      2 
+    29 
+      2 
—      5 
—      1 

—      3 

—      2 
—     3 
+  121 
2 

+    74 
0 
0 
+    15 

II 

+  .21 
—  .87 
—  .76 
—  .02 
—  .14 

—  .25 
+1.41 
—  .93 

+1.72 
+1.44 

—  .34 
—  .65 
—  .86 
—  .27 
—  .13 

—  .14 
—  .07 
—  .01 
+  .22 
—1.  22 

—  .15 

—  .18 
—  .20 
—  .08 
—  .72 

—  .67 
+  .06 
—  .14 
—  .08 
+  .21 

—  .40 
+  .34 
—  .86 
—  .26 

—  .18 

—  .13 
—  .33 

+  .30 
+1.61 
—  .16 

—1.13 
+  .21 
+  .30 
—  .47 
—1.16 

// 

—  .68 
—1.  58 
—2.  17 

—  .80 
—1.02 

+  .41 
+2.  93 
—1.42 

+3.  38 
+3.96 

—1.09 
—2.46 
—2.12 
—1.  64 
—1.79 

—  .68 
—  .07 
—  .67 
+2.20 
—2.79 

+1.  02 
—  .35 
—  .75 
—1.  37 

—2.67 

-1.59 
+  .08 
—4.71 
—  .53 
—  .11 

—1.26 
+  .02 
-2.04 
—  .68 
—  .32 

—  .68 
—1.58 
—1.74 
+3.59 
—  .53 

—6.43 
—  .31 
+1.  42 
—1.86 
—1.52 

7?    Virginia.-   .  

a1   Crucia        .  .  ... 

14  Comse  ...  ..  

4    Draconis  ...  

0    Corvi  

9    Canum  Venaticorum  . 

6.5 
5.5 
3 

2.5 
5 
4.5 
4.5 
5 

1 
3 
6 
6 

4 

5.5 
6 
2.5 
6 
6 

3 
6 
1 
6 
3.5 

5.5 
5 
1 
4 
4 

6 
4 
3.5 
4 
6.5 

I 
4.5 
3 
3 
6.5 

a    Canum  Venaticornm  . 

a    Virginia...  .  

77    Ursse  Majoria  .  ... 

6    Bootia  

7    Bootia  

11  Bootia  .......... 

12  Bootia  

a    Bootia  

"k    Bootis.  . 

6    Bootia  

24  Bootia.  .     . 

p    Bootis.  .  . 

y    Bootia  

5    UrsiB  Minoris  

c3  Centauri  

34  Bootia  

e1   Bootia  

a"  Libras  

[195] 


CATALOGUE  OF  500  STARS. 


601 


for  the  epoch  1875.0 — Continued. 


Number. 

Declination,  1875.0. 

Probable  error 
of  i,  1875. 

4& 

a 

M 

1 

A  . 

'£<=> 
a  o 

*£ 

•—  <  ^ 

cs  n 

§§ 
3V 

Probable  error 
of  annual  va- 
riation. 

dM 
53 

d?i 
dfl 

a 
o 
'S 
o 

a-o 

H  d 

1 

1 

o   /    " 

II 

// 

// 

// 

it 

// 

181 

—  78  37  04.  29 

.22 

2 

—  19.9878 

.0094 

+  323 

+  133 

4-  .  0432 

182 

+  0  01  40.75 

.07 

18 

—  20.  0472 

.0032 

+  349 

+  100 

—  .0278 

183 

—  62  24  21.76 

.25 

1 

—  20.  0219 

.0090 

4-  495 

4-  121 

—  .0417 

'184 

+  27  57  38.99 

.20 

2 

—  20.  0038 

.0056 

+  471 

4-   94 

—  .0270 

*185 

+  69  53  36.  16 

.14 

4 

—  20.  0038 

.0061 

+  505 

4-   66 

—  .0652 

186 

—  22  42  18.75 

.09 

12 

—  19.9725 

.0039 

4-  637 

4-  105 

—  .0659 

187 

+  70  28  38.85 

.10 

9 

—  19.8980 

.0031 

+  548 

4-  61 

4-  .0053 

"188 

4-  41  33  45.55 

.28 

1 

—  19.8729 

.0066 

4-  688 

4-   84 

—  .0232 

189 

+  84  05  32.73 

.11 

8 

—  19.5990 

.0042 

4-  191 

4-   69 

4-  .0128 

"190 

+  56  38  18.77 

.12 

6 

—  19.6318 

.0042 

4-  895 

+   64 

—  .0254 

191 

+  38  59  37.72 

.07 

20 

—  19.5274 

.0027 

4-  970 

4-   76 

4-  .  0481 

•192 

-j-  57  02  25.55 

.30 

1 

—  19.4966 

.0098 

4-  993 

4-  60 

—  .  0246 

193 

—  4  52  16.10 

.07 

16 

—  19.331) 

.  0034 

4-  1319 

+  100 

—  .0412 

194 

4-  28  30  44.08 

.13 

5 

—  18.3458 

.0044 

4-  1220 

+   74 

4-  .  8816 

"195 

4-  40  48  55.48 

.37 

1 

—  19.1607 

.0114 

4-  1:49 

4-   69 

4-  .0161 

196 

—  10  30  29.68 

.06 

26 

—  18.9239 

.0021 

4-  1625 

4-  103 

—  .0378 

197 

4-  55  34  43.01 

.10 

10 

—  18.9095 

.  0031 

4-  1281 

4-   49 

—  .0317 

"198 

+  73  02  27.83 

.22 

2 

—  18.7748 

.0083 

4-  866 

4-  20 

—  .0197 

*199 

-)-  24  52  56.68 

—  18.69-25 

4-  1585 

4-  76 

200 

+  0  02  38.03 

.07 

18 

—  18.5432 

.0031 

4-  1743 

4-  93 

4-  .  0401 

•201 

+  55  59  22.25 

.24 

2 

—  18.5713 

.0084 

+  1365 

4-   44 

—  .0208 

*202 

4-  41  42  58.88 

.34 

1 

—  18.  1897 

.0110 

4-  1672 

4-  56 

—  .0485 

203 

4-  49  56  15.80 

.06 

24 

—  18.  1020 

.0021 

4-  1570 

+  46 

—  .0245 

204 

+  21  53  07.  12 

.24 

9 

—  18.0229 

.0076 

4-  1892 

+   74 

4-  .  0093 

*205 

4-  18  32  58.49 

.27 

1 

—  17.9231 

.  0062 

4-  1965 

+   76 

—  .  0247 

206 

4-  19  01  30.42 

.07 

21 

—  18.2001 

.0028 

4-  1979 

+   75 

—  .  3009 

*207 

+  79  36  44.94 

.23 

2 

—  17.7777 

.0093 

—  133 

4-  124 

—  .  0092 

208 

—  59  46  07.  14 

.23 

2 

—  17.6344 

.0091 

+  2997 

+  218 

—  .  0531 

*209 

4-  27  59  28.11 

.16 

4 

—  17.5600 

.0047 

4-  1998 

4-   65 

+  .  0007 

210 

4-  64  58  25.33 

.07 

17 

—  17.3174 

.1028 

4-  1262 

+   27 

+  .  0059 

211 

4-  25  41  04.  84 

.25 

1 

—  17.2238 

.0116 

4-  2142 

+   6, 

—  .  0656 

"212 

4-  70  01  10.40 

.19 

3 

—  16.9961 

.0081 

+  933 

+   33 

—  .0708 

213 

+  19  50  02.58 

.06 

27 

—  18.9148 

.0020 

4-  2151 

+   66 

—  J.9994 

214 

+  46  39  47.01 

.13 

6 

—  Hi.  6817 

.0043 

4-  1868 

+   41 

4-  .  1548 

215 

+  52  25  45.  12 

.09 

11 

—  16.7873 

.  0032 

+  1767 

4-   34 

—  .4072 

'216 

+  50  24  1H.  17 

.24 

2 

—  16.2565 

.0060 

+  1833 

4-   33 

—  .  0468 

217 

+  30  55  15.53 

.09 

11 

—  15.9845 

.0040 

+  2313 

+   53 

+  .  1132 

218 

+  38  51  21.  11 

.15 

4 

—  15.9247 

.0041 

4-  2170 

4-   45 

4-  .  1416 

219 

+  76  .15  06.01 

.09 

10 

—  16.0100 

.0031 

—  108 

4-  106 

+  .  0159 

*220 

+  47  20  04.78 

.36 

1 

—  15.9744 

.0109 

+  2009 

+   37 

—  .0393 

221 

—  60  19  11.63 

.23 

2 

—  15.  4245 

.0090 

+  3347 

+  176 

+  .  4257 

222 

+  27  03  36.91 

.25 

1 

—  15.4814 

.0069 

+  2515 

+   55 

—  .0031 

223 

+  27  36  07.83 

.07 

20 

—  15.3787 

.0028 

4-  2515 

+   54 

+  .  0102 

224 

—  15  31  15.67 

.07 

21 

—  15.2156 

.0024 

+  3224 

+  100 

—  .0786 

*225 

+  38  19  37.78 

.25 

1 

—  15.0076 

.0094 

+  2302 

4-   41 

+  .1158 

N  B- 


-76 


602 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[196] 


Catalogue  of  500  stars 


Number. 

a 

0 

a 

.    tH 

0,2 

««! 
m 

Name. 

Magnitude. 

Approximate 
right  ascen- 
sion, 1875.0. 

.3 
'E   . 

C3    O 

*  a 

13  9 
0.2 
a  -3 
a 

•< 

<P: 
d«2 

A<5 

A/j' 

*226 

4918 

5.5 

ll.   til.       8. 

14  48  16.  1 

s, 
+  1.517 

8. 

+      9 

// 
—  .69 

n 
—2  51 

2-27 

4936 

ft    Ursae  Minoris  . 

3 

51  05.4 

—  0.  246 

+  103 

4-  .39 

4-1  54 

*228 

4937 

6 

52  14.  1 

+  1.984 

+      1 

—  .05 

—1  43 

2-29 

4958 

3 

57  14.2 

4-  2.260 

0 

—  .27 

—    73 

"230 

4974 

443Bootis  

5 

59  40.  3 

-f-  1.979 

+      1 

—  .05 

—  .64 

*231 

5026 

6 

15  08  50.  0 

-f  2.284 

+      1 

—  .47 

1  13 

232 

5024 

3    Serpentis..  ..  

6 

08  58.  7 

+  2.979 

+      1 

—  .18 

—    46 

233 

5034 

2  5 

10  16  9 

4-  3  220 

4-    12 

—    24 

49 

234 

5'  71 

6 

16  24.7 

-f-  1.759 

+      5 

—  .51 

—  2  10 

235 

5004 

ft1   Boot  is.  ......  .... 

4 

19  46.2 

4-  2.268 

+      1 

—  .56 

—1  06 

236 

5094 

3  5 

20  56  5 

—  0  144 

-L    75 

51 

1  03 

"237 

5097 

£     Draconia  .  .  

3 

22  09.  1 

4-  1.325 

4-     14 

4-    00 

—    53 

238 
•239 

5098 
5115 

/3    CoronsB  Borealis  

4 
6 

22  40.  6 
25  2  '.  9 

+  2.476 
4-  1.  179 

+      2 
4-     17 

4-  .34 

+  .38 

—  .65 
4-1  51 

240 

5122 

vl   Bootis..--  

5  5 

26  26.  4 

4-  2.  153 

4-      2 

4-  .03 

—    20 

241 

5130 

v3  Bootis  

5  5 

27  18.6 

-f  2.  145 

4-      2 

4-  .58 

—    03 

242 

5131 

6    Coronas  Borealis  .  

4  5 

27  53  4 

4-  2.414 

4-      2 

—  .22 

—  2  17 

243 

5143 

2  5 

29  23  8 

4-  2.539 

j.    a 

—  .37 

—    77 

244 

5157 

6 

30  52  9 

4-  2.056 

4-      3 

—    21 

—    59 

245 

5168 

5  5 

33  20.3 

4-  2  154 

4-      2 

—  1  08 

—  2  50 

*24G 

5178 

£    CoronSB  Borealis  .  

5 

15  34  40  3 

4-  2  257 

4-      2 

—    19 

18 

247 

5192 

y    Corona}  Borealis  .  

5 

37  29  7 

-|-  2  518 

4-      3 

4-    26 

3  96 

248 

5196 

a    Serpeutis  .     

2  5 

38  06  7 

4-  2  951 

4-      6 

—  .20 

71 

249 

5216 

ft    Sorpentis  .  .  

3  5 

40  24  9 

4-  2  765 

4-      4 

4-1  01 

1  77 

250 

5245 

3 

44  35  2 

4-  2  987 

4-      7 

—  .66 

1  19 

*251 

5271 

if    Herculis 

6 

48  21  2 

4-  2  071 

4.      2 

4-1  06 

4-2  99 

252 

5285 

f    Ursaa  Minoris 

4 

48  3:i  9 

2  281 

4-  203 

11 

4-     14 

253 

5298 

4    Herculis    .   ,  .   . 

6 

51  18  2 

4-  2  019 

4-      4 

—    21 

1  07 

254 
255 

5302 
5303 

e    Coronas  Borealis  
6    Scorpii  

4.5 
3 

52  24.  9 
52  56  6 

4-  2.485 
-j-  3  537 

4-      3 
4-     16 

—1.59 
—    24 

—2.  75 
2  65 

"256 

5313 

5  5 

54  49  4 

4-  1  410 

4-    10 

4-    28 

4-1  32 

257 

5329 

/31  Bcorpii   .  .  .  . 

2 

58  10  2 

4-  3  477 

4-     14 

16 

5  JJQ 

258 

5341 

5  5 

58  54  2 

4-  1  525 

4-      9 

4-    72 

4-1  60 

259 

5348 

3 

59  33  0 

4-  1  119 

4-     14 

4-    27 

4-    68 

260 

5388 

5 

16  04  49  9 

4-  1  884 

4-      5 

4-    07 

40 

261 

5406 

5 

05  59  1 

4-  0  134 

4-    40 

4-    18 

—    10 

*262 

5415 

6 

06  36  1 

4-  1  170 

4-     14 

32 

2  70 

263 

5414 

<J    Ophinchi  .. 

3 

07  47  8 

_|_  3  138 

4-      8 

25 

4-     16 

264 

5426 

16  Hercul  is  

6  5 

09  56  3 

4-  2  655 

4-      4 

4-    07 

—  2  11 

*265 

54GO 

6 

15  38  1 

4-  2  048 

4-      4 

4-    69 

4-1  90 

266 

5463 

T    Hercnlis  

4 

15  58  9 

+  1  798 

4-      5 

35 

34 

267 

5466 

72  Hercnlis  

3.5 

16  21  4 

+  2  644 

4-      4 

—    08 

80 

268 

5473 

f    Coronse  

5 

17  13  7 

-f  2  343 

4-      3 

—    28 

1  64 

269 

5484 

23  Herculis. 

6 

18  08  6 

+  2  302 

_L         Q 

+     12 

1  3° 

•270 

5502 

5 

21  41  5 

-)-  1  309 

4-     10 

4-1  15 

4-3  46 

[197] 


CATALOGUE  OF  500  STAES. 


603 


for  the  epoch  1875.0 — Continued. 


Number. 

Declination,  1875.0. 

Probable  error 
of  6,  1875. 

*5 
§ 

1 

Annual  varia- 
tion, 1875.0. 

Probable  error 
of  annual  va- 
riation. 

dP<5 
W 

<P(J 
<W 

Proper  motion 

in  '  . 

o   /    // 

it 

// 

ii 

a 

// 

it 

•226 

+  59  48  09.67 

.25 

1 

—  14.7446 

.0082 

+  1531 

-f   25 

+  .  1429 

227 

4-  74  39  58.82 

.06 

23 

—  14.7165 

.0021 

—  187 

+  103 

4-  .  0044 

•228 

4-  50  08  25.  11 

.25 

1 

—  14.8935 

.0083 

+  2043 

4-   30 

—  .2408 

229 

+  40  53  04.27 

.08 

14 

—  14.3957 

.0035 

-f  2359 

+   37 

—  .0453 

•230 

4-  48  08  30.91 

.23 

2 

—  14.  1601 

.  0065 

+  2057 

4-   28 

4-  .0406 

"231 

4-  38  44  02.28 

.27 

1 

—  13.  6428 

.0114 

+  2504 

+   36 

—  .0193 

232 

4-  5  24  17.12 

.23 

2 

—  13.6369 

.  0075 

+  3249 

+   68 

—  .0226 

233 

—  8  55  13.00 

.07 

20 

—  13.5611 

.0029 

+  3518 

4-   84 

—  .0309 

234 

4-  52  24  33.59 

.33 

1 

—  13.  1505 

.017 

-f  1996 

+   25 

—  .021 

235 

-f  37  48  59.73 

.10 

9 

—  12.8177 

.0033 

4-  2575 

4-   34 

4-  .0884 

236 

+  72  16  43.62 

.08 

14 

—  12.8097 

.0024 

—  107 

+   84 

4-  .  0177 

•237 

4-  59  24  16.68 

.09 

13 

—  12.7252 

.0042 

+  1547 

4-   26 

4-  .  0207 

238 

4-  29  32  15.34 

.19 

3 

—  12.6428 

.0057 

+  2836 

4-   41 

4-  .  0675 

•239 

+  61  OC  07.  12 

.31 

1 

—  12.5392 

.0103 

+  1397 

4-   28 

—  .0129 

240 

4-  41  15  36.63 

.24 

2 

—  12.4559 

.0081 

4-  2515 

+   31 

—  .0020 

241 

+  41  19  28.32 

.24 

2 

—  12.4035 

.0070 

+  2509 

+   30 

—  .0093 

242 

+  31  46  55.88 

.26 

1 

—  12.3759 

.0090 

4-  2820 

4-   39 

—  .0217 

243 

4-  27  08  11.55 

.OB 

25 

—  12.3498 

.0021 

+  2995 

4-   42 

—  .0997 

244 

+  43  34  56.59 

.23 

2 

—  12.  1038 

.0095 

4-  2433 

4-   28 

4-  .  0431 

245 

-f  40  45  41.21 

.23 

2 

—  11.9172 

.0065 

+  2577 

4-   30 

4-  .  0580 

•246 

+  37  02  33.81 

.20 

2 

—  11.8762 

.0067 

4-  2700 

4-   32 

4-  .  0052 

247 

4-  26  41  33.  66 

.19 

3 

—  11.6641 

.0054 

+  3027 

+   40 

4-  .0174 

248 

+  6  49  12.87 

.06 

24 

—  11.6037 

.  0022 

4-  3565 

4-   58 

4-  .  0339 

249 

4-  15  48  52.01 

.19 

3 

—  11.5206 

.0052 

4-  3360 

+   49 

—  .0477 

250 

-f  4  51  19.62 

.10 

10 

—  11.  1035 

.0039 

+  3677 

+   58 

4-  .0681 

"251 

+  42  48  08.07 

.26 

1 

-  10.2901 

.  0063 

-f-  2629 

4-   24 

4-  .6159 

252 

4-  78  10  40.77 

.07 

18 

—  10.8824 

.0024 

—  2731 

4-  280 

—  .0016 

253 

-j-  42  55  49.89 

.34 

1 

—  10.6895 

.0099 

4-  2539 

4-   25 

—  .0107 

254 

+  27  14  27.75 

.15 

4 

—  10.6578 

.0053 

+  3120 

4-   36 

—  .0615 

255 

—  22  15  50.64 

.10 

9 

—  10.5934 

.0046 

+  4429 

4-   82 

—  .0365 

•256 

+  55  06  13.  04 

.22 

2 

—  10.3006 

.  0089. 

+  1772 

+  21 

—  .1162 

257 

—  19  27  41.36 

.08 

16 

—  10.  2034 

.0032 

-f  4413 

4-  75 

—  .0380 

258 

4-  53  15  49.  12 

.59 

—  10.0441 

.016 

4-  1961 

4-  21 

—  .034 

259 

+  58  53  58.60 

.11 

8 

—  9.  7203 

.0030 

+  1408 

4-  22 

—  .3408 

260 

+  45  15  48.77 

.16 

3 

—  9.6258 

.0051 

+  2443 

4-   22 

—  .0330 

261 

+  68  08  22.63 

.16 

3 

—  9.5012 

.0065 

+  204 

4-   52 

4-  .0690 

•262 

+  58  15  50.87 

.35 

1 

—  9.4827 

.023 

-f  1542 

4-   23 

'4-  .040 

263 

—  3  22  14.98 

.07 

17 

—  9.5740 

.  0032 

4-  4075 

+   56 

—  .1434 

264 

+  19  07  29.87 

.23 

2 

—  9.  3579 

.0113 

-f-  3466 

4-   37 

—  .0931 

•265 

-j-  40  00  31.66 

.49 

—  8.  8149 

.014 

-j-  2699 

4-   22 

4-  .005 

266 

+  46  36  42.79 

.10 

9 

—  8.7700 

.0037 

-f  2391 

4-   20 

4-  .0226 

267 

+  19  26  53.32 

.13 

6 

—  8.7062 

.0043 

4-  3502 

+   34 

4-  .  0530 

268 

4-  31  10  59.72 

.20 

2 

—  8.5928 

.  0065 

-f  3116 

4-   26 

4-  .  1016 

269 

+  32  37  33.02 

.22 

2 

—  8.6424 

.0076 

-f  3072 

4-   26 

4-  .0092 

•270 

4-  55  29  24.26 

.25 

1 

—  8.3192 

.0090 

4-  1765 

4-   20 

4-  .  0216 

604 


UNITED  STATES  NOETHERN  BOUNDARY  COMMISSION. 


[198] 


Catalogue  of  500  stars 


Nnmber. 

s 

.  p 
a 

dj 
^ 

« 

Name. 

Magnitude. 

Approximate 
right  ascen- 
sion, 1875.0. 

i 

ej 

ll 

g* 

<! 

<Pa 
IP 

M 

v 

271 

5498 

1 

h.  m.    s. 
15  21  44.7 

8. 

+  3.668 

s. 
4-     15 

ll 
—  .18 

11 

—    67 

272 

5512 

ij    Draconis  ...  

3 

22  18.2 

4-  0.  805 

-f    18 

4-  .06 

—  .54 

•273 

5523 

5 

24  32.3 

4-  1.968 

+       4 

—1.35 

—3.74 

274 

5520 

4 

24  36.6 

+  3.024 

-f      6 

—  .07 

—  1  42 

275 

5535 

34  Herculis  

6.5 

£6  40.2 

4-  1.644 

+      6 

4-  .75 

4-1.28 

*276 

5545 

15  Draconis  .  .  .  .    .. 

4.5 

28  14.3 

—  0.  141 

+    41 

.00 

—     41 

277 

5541 

6 

28  37.0 

+  2.332 

+      3 

4-  .65 

—     47 

278 

5552 

tr    Herculis  .  .. 

4 

30  04.5 

4-  1.932 

4      4 

—  .05 

4-    40 

279 

5548 

C    Ophiuchi  .     

3.5 

30  16.6 

4-  3.298 

+      9 

—1.65 

—2  58 

280 

5568 

6 

32  32.4 

4-  1.741 

+      5 

4-  .93 

4-1  16 

281 

5596 

42  Herculis  .  .  

5 

16  35  21.4 

4-  1.625 

4-      6 

4-  .27 

—  .41 

282 

5578 

o    Triangnli  Aust.  .  . 

2 

35  26.  9 

4-  6.287 

+    91 

—  .09 

—1  63 

283 

5604 

C    Herculis  .  

3 

36  34.5 

4-  2.263 

+      3 

—  .14 

—    (0 

284 

5617 

i]    Herculis  ...     .  . 

3 

38  36.7 

+  2.055 

+      4 

—1.44 

—2  63 

*2ri5 

5624 

7 

40  06.7 

+  2.385 

+       3 

4-  .20 

4-1  11 

286 

5643 

5 

42  55.7 

4-  1.134 

+   10 

—  .21 

—1  85 

*287 

5644 

6 

43  19.8 

+  1.914 

+      4 

—  .23 

—    60 

*2s'8 

5658 

6 

44  17.8 

4-  1.237 

•4-     10 

4-  .09 

-t-    84 

•289 

5693 

5 

48  13.6 

+  2.269 

4-      3 

.00 

—  1  00 

290 

5706 

6 

50  43.9 

4-  1.721 

+      5 

—1.38 

—4  12 

291 

5708 

4 

51  45.  1 

+  2.835 

4-      4 

—  .21 

—    86 

292 

5731 

e     Herculis  ... 

3 

55  30  5 

4-  2.293 

4-      3 

—  .34 

—2  15 

293 

5747 

59  Herculis  ...  - 

5 

56  59.3 

+  2.209 

4-      3 

—1.49 

—2  89 

294 

5780 

s    Ursse  Minoris  

4 

58  50.  9 

—  6.  376 

4-  307 

4-  .02 

—    59 

295 

5776 

0 

17  01  31.0 

-f  1.594 

4-      6 

—  .01 

4-2  89 

296 

5778 

?1    Scorpii  .  ... 

3.5 

03  12.1 

4-  4.286 

4-     17 

—  .25 

4-    57 

297 

5801 

6 

05  23  9 

+  1.  151 

4-      8 

4  .90 

4-3  90 

*298 

5823 

f    Draconis.  _. 

3 

08  25.7 

4-  0.  162 

4-    19 

—  .02 

_L    28 

299 

5821 

a1  Herculis  ..... 

3.5 

08  56.9 

+  2.733 

4-      3 

4-  .  13 

—    26 

300 

5834 

TT    Herculis  .  ...... 

3.5 

10  41.6 

4-  2.087 

4-      3 

—  .06 

—    87 

301 

5847 

4.5 

13  21.6 

-|-  2.030 

4-      3 

—  .68 

—3  69 

*302 

5853 

6 

13  37  8 

+  1.527 

4-      5 

—  .56 

—  4  18 

303 

5874 

6 

17  37  6 

4-  1.968 

4-      4 

—  .29 

+    93 

304 

5876 

5 

18  44  2 

-f-  3  657 

4-      7 

—  .55 

—1  11 

305 

5886 

4 

19  22  2 

4-  2.070 

4-      3 

—  .10 

-1  02 

*306 

5911 

77  Herculis  

5.5 

23  25.4 

4-  1.586 

4-      4 

—  .30 

4  .01 

307 

5918 

6 

24  12.5 

4-  0.895 

4-      8 

4-  .50 

4-1.99 

308 

5937 

2.5 

27  3f  5 

4-  1.351 

4-      5 

4  .05 

—  .06 

309 

5941 

o    Ophiuchi  

2 

29  08.0 

4-  2  78sJ 

4-      3 

—  .22 

—1.11 

310 

5997 

6 

36  50  6 

4-  1  815 

4-      3 

4     37 

00 

311 

6006 

u   Draconis  

4 

37  41.1 

—  0  355 

+     11 

4-  .46 

+1.97 

312 

6021 

/i    Herculis...... 

4 

41  34  0 

4-  2  345 

4      4 

40 

1  49 

313 

6033 

S7  Herculis  

6 

43  45  0 

4-  2  430 

J_      ;j 

—    13 

1  17 

314 

6036 

7 

43  46  7 

4-  1  613 

4-      3 

4     19 

4-1  30 

'315 

6047 

^i1  Draconis  .......  . 

4  5 

44  09  9 

—  1  082 

-L          2 

-j-    08 

41 

[199] 


CATALOGUE  OF  500  STAKS. 


605 


for  the  epoch  1875.0 — Continued. 


Number. 

Declination,  1875.0. 

Probable  error 
of  d,  1875. 

*J 

1 

0> 

Annual  varia- 
tion 1875.0. 

Probable  error 
of  annual  va- 
riation. 

$>& 
dt" 

M 

dt3 

a 
o 
•-3 
o 
i-d 

t>  a 

IT 

8 
fi 

o   /    n 

II 

// 

u 

ft 

u 

:/ 

271 

—  26  09  09.  18 

.09 

11 

—  8.  3734 

.0041 

+  4900 

4-  71 

—  .0367 

272 

4-  Cl  47  51.  11 

.07 

17 

—  8.2376 

.0026 

4-  1107 

4-   26 

4-  .  0546 

•273 

4-  42  09  28.  15 

.27 

1 

—  8.1111 

.0083 

+  2656 

4-   20 

4-  •  0026 

274 

+  2  15  32.64 

.11 

8 

—  8.2062 

.0043 

4-  4068 

4-   44 

—  .  0982 

275 

4-  49  14  02.  15 

.43 

—  8.  0040 

.0109 

+  2230 

4-   18 

—  .0612 

•276 

4-  69  02  18.29 

.13 

6 

—  7.7958 

.0047 

—  157 

4-   55 

4-  .  0209 

277 

-j-  30  45  45.25 

.20 

2 

—  7.  7908 

.0106 

+  3158 

4-   24 

—  .  0047 

278 

-f  42  41  45.08 

.12 

6 

—  7.6334 

.0041 

+  2637 

4-   19 

4-  .  0350 

270 

—  10  11  43.56 

.11 

8 

—  7.6308 

.0047 

+  4480 

4-  52 

+  .  0212 

280 

4-  46  52  01.93 

.40 

1 

—  7.  4570 

.0116 

4-  2379 

+   17 

-t-  .  0116 

281 

+  49  10  25.04 

.19 

2 

—  7.2184 

.  0052 

+  2335 

+   17 

4-  .  0209 

282 

—  68  47  39.  59 

.22 

2 

—  7.2882 

.0094 

4-  8085 

4-  268 

—  .  0563 

283 

4-  31  49  49.47 

.08 

15 

—  6.  7387 

.0032 

+  3068 

+   20 

4-  .4010 

284 

+  39  09  39.91 

.10 

9 

—  7.  0633 

.0030 

+  2844 

4-   19 

—  .0903 

*285 

4-  28  35  15.28 

.30 

1 

—  6.8077 

.0087 

4-  3302 

+   22 

4-  .  0421 

286 

+  57  00  20.98 

.16 

4 

—  6.5672 

.  0103 

+  1596 

+   17 

4-  .  0505 

*287 

4-  42  27  45.06 

.29 

1 

—  6.6194 

.0104 

4-  2668 

+   16 

—  .  0350 

*288 

+  55  37  54.  61 

.29 

1 

—  6.5260 

.0122 

+  1751 

+   17 

—  .  0216 

"289 

+  31  54  35.34 

.19 

2 

—  6.2002 

.0056 

+  3159 

+   19 

—  .  0220 

290 

4-  46  44  31.22 

.34 

1 

—  6.0105 

.0131 

4  2428 

+   14 

—  .0412 

291 

+  9  34  15.45 

.07 

19 

—  5.8897 

.0032 

+  3947 

4-   27 

—  .0056 

292 

4-  31  06  42.  18 

.10 

9 

—  5.5476 

.0042 

4-  3230 

4-   17 

4-  .  0215 

293 

4-  33  45  01.75 

.15 

4 

—  5.4424 

.  0058 

+  3120 

4-   16 

4-  .  0021 

294 

4-  82  14  22.49 

.07 

18 

—  5.2906 

.0028 

—  8926 

4-  552 

—  .0029 

295 

4-  48  58  37.  19 

.30 

1 

—  5.153S 

.0113 

+  2285 

+   13 

—  .0911 

296 

—  43  04  17.  25 

.29 

1 

—  5.1936 

.0109 

4-  6083 

4-   63 

—  .2743 

297 

4-  55  55  38.90 

.48 

—  4.  6937 

.014 

4-  1652 

4-   14 

4-  .039 

*298 

4-  05  52  06.96 

.11 

7 

—  4.4578 

.0039 

+  251 

n   *^ 
4-   27 

4-  .0168 

299 

+  14  32  03.76 

.06 

23 

—  4.  4039 

.  0022 

4-  3905 

4-   19 

4-  .  0204 

300 

4-  36  57  03.65 

.11 

7 

—  4.2959 

.0050 

4-  2987 

4-   12 

—  .  0147 

301 

+  37  25  24.62 

.18 

3 

—  4.0069 

.0049 

4-  2920 

4-  U 

4-  .  0461 

*302 

4-  49  49  33.75 

.30 

1 

—  4.0157 

.  0123 

4-  2190 

+  10 

4-  .0142 

303 

+  40  05  54.51 

.26 

1 

—  3.7564 

.0100 

+  2840 

4-  10 

—  .0697 

304 

—  24  03  29.  05 

.13 

6 

—  3.7222 

.0060 

+  5260 

4-  27 

—  .1311 

305 

+  37  15  43.15 

.11 

7 

—  3.5458 

.0042 

+  2985 

4-  10 

—  .0092 

"306 

+  48  21  56.68 

.18 

3 

—  3.2029 

.0058 

4-  2299 

4-   9 

—  .  0159 

307 

4-  58  45  24.50 

.25 

1 

—  3.0992 

.0110 

+  1303 

•  +  12 

4-  .  0199 

308 

4-  f>2  23  40.57 

.07 

17 

—  2.8255 

.0025 

4-  1959 

4-   8 

—  .  0006 

309 

4-  12  39  09.44 

.06 

24 

—  2.9299 

.0022 

4-  4044 

4-   12 

—  .2371 

310 

4-  43  31  58.67 

—  1.  9728 

4-  2650 

4-   6 

4-  .050 

311 

4-  68  48  5S.74 

.11 

7 

—  1.6258 

.0041 

—  499 

1 

4-   14 

4-  .  3237 

31-2 

4-  27  47  42.  17 

.07 

20 

—  2.  3701 

.0031 

4-  3380 

4-   8 

—  .7589 

313 

+  25  39  56.97 

.18 

3 

—  1.4703 

.0057 

+  3538 

4-   5 

—  .0497 

314 

4-  47  39  22.  19 

.41 

1 

—  1.  4053 

.014 

4-  2358 

4-   5 

4-  .013 

*315 

+  72  12  34.25 

.11 

7 

—  1.6576 

.0040 

—  1565 

4-   30 

—  .2731 

606 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[L'OOJ 


Catalogue  of  500  stars 


"l 
Number. 

§ 

s 
a 

dj 
< 
ri 

Name. 

Magnitude. 

Approximate 
right  ascen- 
sion, 1875.0. 

OJ 

'go 
>_a 

'a  a 
s  o 
a'S 
a 
*4 

<Pa 

30 

A<! 

A/ 

31(5 

6056 

6 

h.  m.     s. 
17  46  47  1 

s. 
+    1.  567 

s. 
+        3 

// 
05 

// 
1  39 

*317 

6073 

H9    Herculis 

5  5 

50  22  7 

+    2.  420 

4-         2 

—     20 

96 

318 

6079 

3  5 

51  22  1 

+     1.  036 

4-        4 

4-1  05 

+1  02 

319 

6082 

0      Ilerculis 

4 

51  57  9 

+    2  053 

•4-        2 

47 

1  83 

320 

6091 

a 

55  42  4 

4-     1  394 

-4-         3 

4-     04 

4-     28 

*321 

6114 

35    Draconis 

5 

55  02  6 

—    2.696 

-4-        6 

4-     24 

4-     84 

322 

6115 

y3     Sagittarii    . 

4 

57  46  7 

-f    3.  852 

-t-        2 

4-     07 

4-     15 

323 

6150 

4 

02  40  0 

-f-     2.  338 

-t-        2 

4-     43 

Bfi 

*324 

6157 

102  Hercnlis 

5  5 

03  24  7 

+    2  560 

-t-        2 

—    41 

1  69 

325 

6168 

//      Sagittarii  . 

3  5 

06  17  2 

-f-    3  584 

J_        i 

—    38 

18 

*3°6 

6206 

5 

18  09  2:!  4 

—    4  470 

26 

4-     50 

4-3  24 

307 

6216 

6 

12  30  0 

-f     1  062 

4-        1 

-4-     4f! 

4-1   ",0 

328 

6281 

(I      Ursae  Minoris    . 

3 

12  39  3 

—  19  420 

—    385 

4-     17 

-j-     185 

329 

6229 

77      Serpent  is  . 

4 

14  50  5 

-f    3.  100 

+        2 

-i-     12 

o.i 

330 

5959 

a      Octantis 

6 

15  28  5 

+109.  058 

—  11035 

_|_     08 

—    76 

*331 

6245 

6 

17  17  6 

4-    2  645 

-L            ^ 

4-     55 

+1  70 

*332 

6268 

u      Ijvraj 

5  5 

20  06  8 

+     1  974 

4-        2 

65 

1  2-> 

*333 

6289 

39    Draconis 

5 

22  04  9 

-f-    0  874 

0 

18 

4-     22 

3:>4 

6302 

X      Draconis 

4  5 

23  18  6 

—     1  075 

9 

15 

1  56 

'335 

6318 

jj 

25  58  8 

-f     0  820 

j 

+     38 

4-1  61 

336 

6325 

1      AqnilsB  . 

5  5 

28  24  3 

4-     3  272 

0 

-f    05 

g.» 

337 

6355 

a      Lyras 

1 

32  42  4 

4-    2  031 

4-        1 

00 

—  1  16 

*338 

6365 

6 

35  58  1 

4-    2  036 

4-         2 

12 

48 

339 

6390 

e1     L/yrse 

5 

40  11  9 

4-    1  986 

_L        i 

76 

04 

340 

6387 

110  Herculis 

5 

40  17  0 

4-    2  582 

4-        2 

+    08 

4-     (>5 

341 

6397 

111  Hercnlis 

5  5 

41  30  1 

4-     2  649 

_i_        i 

-)-     03 

—  1  29 

»342 

6421 

6 

44  16.0 

4-     1.  547 

0 

+  .35 

+2*08 

343 

6429 

/3     Lyrai  

3 

45  27.9 

+    2.  214 

-L            1 

—  .53 

—2  51 

344 

6440 

a      Sagittarii.  ..  

3 

47  30.8 

-f    3.  723 

^ 

—    03 

+    2H 

345 

6463 

5 

49  21  4 

-f     0.  887 

4 

00 

—    62 

346 

6478 

50    Draconia 

5 

50  23  6 

1  901 

55 

+1  18 

+1  65 

*347 

6476 

6 

51  29  3 

4-    1  580 

o 

+1  45 

4-1  54 

348 

6487 

e       Auiiihr  . 

3  5 

53  57  0 

+    2  721 

_i_        i 

05 

4-     74 

349 

6491 

y      Lvrse  . 

3 

54  16  0 

-f-    2  242 

4-         1 

50 

—  1  3H 

350 

6526 

X      Aquilse  

3 

59  36  9 

-f     3  184 

—        2 

16 

—     57 

351 

6528 

f      AquilsB 

3 

18  F9  39  8 

-J-    2  755 

0 

—    OS 

—  1  03 

•352 

6553 

17    Lyra}  

e 

19  02  42  0 

+    2  266 

4.         i 

12 

—     42 

•353 

6586 

55    Draconis  .. 

6 

09  17  7 

-f    0  238 

—      17 

-f-     24 

4-     56 

354 

6584 

43    Sagittarii  

5 

10  19  2 

4-     3  514 

—        6 

—  3  50 

—  5  74 

355 

6585 

22    Aqnilffi  

6 

10  19  9 

-f-    2  969 

—        1 

73 

—  1  78 

3C6 

6C12 

<5      Draconis  .   .  . 

3 

12  31  3 

+    0  033 

—      23 

4-     25 

4-    74 

357 

60-J8 

K      Cvuni  .  . 

4 

14  12  8 

+     1  388 

—        3 

—     14 

4-    40 

•358 

6024 

6 

14  47  4 

+    2  005 

—        I 

—    04 

-(-     60 

359 

6650 

T      Draconis  .  .-  

4.5 

17  56  7 

—     1  108 

—      58 

4-    70 

+1  06 

360 

6646 

S         Ai|llil;r  

3.5 

19  11.7 

-f    3.024 

_        2 

-4-     11 

4-     03 

[201] 


CATALOGUE  OF  600  STAES. 


607 


for  the  epoch  1875.0 — Continued. 


Number. 

Declination,  1875.0. 

Probable  error 
of  S,  1875. 

-»• 
Ji 

.3° 

*S 

£ 

Annual  varia- 
tion, 1875.0. 

Probable  error 
of  annual  va- 
riation. 

(Pi 
0 

<Pt 
di" 

a 
.2 
"o 
|<4 

•~  o 

3;  •*• 

CL, 
1 

O      1      II 

a 

// 

a 

tt 

it 

// 

316 

+  48  25  43.42 

.22 

2 

—  1.1526 

.0063 

-f  2287 

+    4 

+  .  0031 

•317 

+  26  04  16.59 

.14 

5 

—  0.8413 

.0065 

+  3528 

+   3 

+  .  0004 

318 

4-  56  53  34.27 

.16 

4 

—  0.6840 

.0048 

+  1530 

+    4 

•+  .0712 

319 

+  37  16  05.73 

.23 

2 

—  0.6902 

.0060 

+  2992 

+   3 

4-  .  0127 

3-20 

-f  51  30  15.44 

.07 

20 

—  0.5808 

.0023 

+  2037 

+    4 

—  .0302 

"321 

+  76  58  40.25 

.18 

3 

—  0.1901 

.0052 

—  3913 

+   14 

+  .2434 

32-2 

—  30  25  23.  53 

.18 

3 

—  0.4128 

.0086 

4-  5612 

0 

—  .  2185 

323 

+  28  44  47.  53 

.21 

2 

+  0.  2247 

.0064 

-f  3408 

0 

—  .0086 

*324 

-f  20  47  45.96 

.25 

1 

+  0.2617 

.0076 

+  3738 

—   1 

—  .  0369 

325 

—  21  05  21.58 

.08 

14 

+  0.5383 

.  0036 

+  5216 

—    7 

—  .  0118 

»326 

+  79  58  54.77 

.21 

2 

+  0.9408 

.0062 

—  6486 

—   44 

-r-  .1194 

327 

-f  56  32  47.26 

.54 



+  1.1722 

.015 

+  1556 

0 

+  .079 

328 

+  86  36  27.58 

.06 

24 

4-  1.  1574 

.0020 

—  28-244 

—  768 

4-  .  0506 

32!) 

—  2  55  45.52 

.10 

9 

4-  0.  6245 

.0012 

+  4448 

—   r 

—  .  6732 

330 

—  89  16  38.77 

.15 

4 

+  1.3297 

.0067 

+159005 

—24722 

—  .0236 

•331 

-f  17  45  53.82 

.39 

1 

+  1.  4948 

.022 

+  3840 

—    7 

—  .017 

*332 

+  39  26  24.24 

.22 

2 

4-  1.7474 

.0054 

4.  2864 

—   3 

—  .0102 

•333 

-j-  58  43  43.56 

.23 

2 

+  1.9835 

.0064 

+  1250 

—   2 

+  .  0542 

334 

-)-  72  40  40.  95 

.12 

6 

+  1.  6566 

.0037 

—  1401 

—   9 

—  .3796 

•335 

+  59  27  58.88 

.21 

2 

+  2.3026 

.0089 

+  1179 

—   4 

-f  .0341 

336 

—  8  19  .16.61 

.11 

8 

+  2.  1489 

.0040 

+  4733 

—   18 

—  .  3302 

337 

+  38  40  06.  16 

.06 

26 

+  3.  1246 

.  00-20 

+  2946 

—   8 

+  .2724 

•338 

4-  38  15  07.25 

.25 

1 

+  3.1376 

.0094 

+  2912 

—    7 

+  .  0032 

339 

4-  39  32  24.90 

.12 

6 

+  3.  5520 

.0039 

+  2836 

—   8 

+  .0:>23 

340 

-)-  20  25  41.  18 

.18 

3 

-f-  3.  1592 

.0054 

+  3692 

—   13 

—  .3475 

341 

+  18  02  37.70 

.21 

2 

+  3.7118 

.0060 

+  3791 

—   15 

+  .1001 

*342 

+  49  17  39.20 

.30 

1 

+  3.8772 

.0109 

+  2198 

—   6 

+  .0278 

343 

-j-  33  13  07.21 

.06 

22 

+  3.9352 

.  0025 

+  3150 

—   11 

—  .0171 

344 

—  26  26  59.  03 

.12 

7 

+  4.0506 

.0049 

+  5296 

—   42 

—  .0772 

345 

+  59  14  09.28 

.12 

7 

+  4.2994 

.0036 

+  1257 

—   9 

-f  .0138 

346 

+  75  17  07.67 

.12 

6 

+  4.4487 

.0059 

—  2730 

—   86 

+  .  0745 

•347 

+  48  42  14.32 

.56 

...... 

-f  4.  3480 

.0131 

4-  2216 

—   8 

—  .1196 

348 

+  14  54  00.16 

.13 

5 

+  4.5926 

.0045 

4  3831 

—   21 

—  .0846 

349 

+  32  31  09.33 

.11 

7 

+  4.  6905 

.0041 

4  3157 

—   13 

—  .0138 

350 

—  5  04  05.79 

.10 

9 

+  5.0622 

.0041 

+  4462 

—   34 

—  .0957 

351 

-f-  13  40  45.01 

.07 

20 

+  5.  0587 

.0030 

-f  3856 

—   23 

—  .1033 

•352 

+  32  18  21.38 

.23 

2 

+  5.  4360 

.0064 

4  3170 

—   16 

+  .  0178 

•353 

-f  65  46  10.12 

.19 

2 

+  5.9941 

.  0072 

+  303 

—   24 

+  .  0226 

354 

—  19  10  24.  10 

.12 

6 

+  6.0397 

.0045 

4  4855 

—   52 

—  .0174 

355 

+  4  36  57.77 

.41 

1 

+  6.0443 

.0079 

4  4102 

—   33 

—  .0138 

356 

-f  67  26  30.  05 

.08 

16 

+  6.  3259 

.0025 

+   45 

—   32 

+  .0854 

357 

+  53  08  18.45 

.11 

8 

4-  6.4911 

.0035 

+  1901 

—   12 

+  .1100 

"358 

4-  40  07  51.59 

+  6.  4379 

4-  2742 

—   17 

-4-  .009 

359 

4-  73  07  22.  06 

.14 

5 

+  6.7984 

.0051 

—  1589 

—   82 

[—     ,  WUW 

+  .  1086 

360 

+  2  52  01.79 

.07 

19 

+  6.  8691 

.0028 

+  4142 

—   39 

+  .0763 

608 


UNITED  STATES  NOETHEEN  BOUMDAEY  COMMISSION. 


[202] 


Catalogue  of  500  stars 


Number. 

a 

l 

a 
cjj 

«<3 

CQ 

Name. 

Magnitude. 

Approximate 
right  ascen- 
sion, 1S75.0. 

Annual  varia- 
tion in  a. 

&a 
dP 

M 

v 

361 

6657 

5.5 

h.   m.     s. 
19  20  15  4 

8. 

4  2  480 

8. 

4        2 

a 
33 

II 

1  65 

362 

6661 

6.5 

20  45  9 

4  2  619 

4-         1 

_|_     03 

0  04 

•363 

6681 

6.5 

23  31  2 

4  1  090 

6 

07 

-1-     7r> 

364 

6690 

0    Cvcni   . 

3 

25  40  8 

4  2  417 

-L            1 

_|_    06 

04 

365 

6697 

t2    Cvcni  . 

5 

26  33  3 

4  1  514 

2 

_j-    08 

4     55 

396 

6698 

8    Cygui  

6 

27  08.  3 

+  2.234 

4        1 

—    10 

—  1  33 

367 

6713 

K    AquilsB 

4 

30  10  0 

4-  3  230 

—        4 

1  92 

0     JO 

"368 

6728 

5.5 

32  33.9 

+  1.910 

0 

4-    62 

41  70 

3(i9 

6734 

0    Cveni  . 

4 

33  05  4 

4  1  609 

a 

08 

41  15 

•370 

6748 

5 

35  52  7 

_j_  i  356 

n 

4-     17 

41  90 

371 

6758 

10  Vulpeculse.  

6 

38  31.  1 

+  2.493 

JL           I 

—    13 

—  1  45 

372 

6772 

3 

40  19  0 

4-  2  852 

1           1 

08 

34 

*373 

6780 

5 

40  48.6 

+  1.  178 

y 

—    48 

—     57 

374 

6779 

6    Cvffni.  . 

3.5 

41  04.  1 

+  1.876 

o 

—     10 

—  1  12 

375 

6802 

1.5 

44  41.  1 

4  2.928 

—        2 

4     14 

4    31 

*376 

6817 

5 

46  20  0 

-f  2.062 

4.        l 

—    10 

4     05 

*377 

6830 

6 

48  26  2 

-|-  1.763 

0 

—    56 

—     68 

378 

6836 

e    Draconis  ......  

5.5 

48  35.1 

—  0.  173 

—      44 

41  40 

43  11 

379 

6833 

/?    Acjuilse..  

3.5 

49  10.4 

+  2.947 

—        1 

—    34 

—    89 

380 

6999 

(5) 

49  17.8 

—60  647 

—29716 

4    57 

41  16 

381 

6rt56 

ih    Cvfirni  .  . 

5.5 

52  23  9 

-f  1.554 

_        2 

4    20 

43  19 

*382 

0865 

6 

53  19.9 

4  1  639 

—        2 

4    40 

41  50 

383 

6879 

15  Vulpeculte.  .. 

5 

55  57.2 

-f  2  463 

-L            1 

—2  01 

—  5  04 

384 

6893 

T    Aquilse  .    

5.5 

58  02  0 

4  2  933 

—        2 

—  1  33 

—  1  14 

"385 

6937 

28  Cvgni  

5 

20  04  47.2 

4  2  226 

-L           2 

—  1  14 

—  2  53 

*386 

6970 

68  Draconis  .  

6 

09  31  9 

4  0  992 

—      14 

4    51 

42  09 

387 

6965 

o2   Cygni  ......  

4 

09  41  8 

+  1  889 

0 

—    17 

4     17 

388 

6974 

3 

11  07  0 

+  3.331 

—        8 

—    23 

-)-     03 

389 

7005 

K    Cephei  .  .. 

4.5 

13  03  7 

—  1  899 

—    165 

41  28 

42  93 

390 

7004 

2 

15  44  7 

4  4  787 

—      59 

—  •    33 

—  4  02 

*391 

7024 

71  Draconis  . 

6  5 

17  31  3 

4  1  014 

14 

4-    36 

-1      fli 

392 

7022 

y    Cygni  

3 

17  44  5 

4  2.  152 

J-        2 

16 

1  89 

393 

7031 

TT    Capricorni  ...  ... 

5 

20  09  9 

4  3  441 

11 

1  °5 

-1-1   27 

394 

7061 

40  Cygni  

6 

22  56  4 

4  2  241 

-4-        2 

C7 

2  41 

*395 

7073 

42  Cygni  

6 

24  34  4 

4  2  287 

_)_        2 

13 

41  04 

396 

7088 

e    Delphini  

4 

27  14.4 

4-  2.  866 

—        1 

—  .43 

—    19 

397 

7098 

8    Cepbei  

5 

27  28.8 

+  1.016 

—      15 

4  .20 

4    29 

"398 

7100 

6 

28  31  3 

-j-  2  086 

-J-        2 

06 

00 

399 

7124 

5  5 

30  31  9 

—  0  210 

67 

33 

4    24 

400 

7121 

4 

31  41  2 

4  2  811 

o 

23 

1  41 

401 

7140 

29  Vnlpecul»  

5  5 

32  56  3 

4  2  676 

_L             1 

4    44 

88 

402 

7149 

a    Delphini  .  .  

3.5 

33  50  0 

4  2  789 

0 

05 

18 

•403 

7166 

6 

35  46  3 

+  1  560 

3 

17 

4    07 

404 

7171 

a    Cygui  .  ....  . 

1 

37  10  3 

4  2.044 

4-        2 

25 

94 

405 

7173 

6     Delphi  ni 

4 

37  37  4 

4  2  800 

o 

33 

1  fil 

[203] 


CATALOGUE  OF  500  STARS. 


609 


for  the  epoch  1875.0 — Continued. 


Number. 

Declination,  1875.0. 

Probable  error 
of  <!,  1875. 

1 
3 

f 

Annual  varia- 
tion, 1875.0. 

Probable  error 
of  annual  va- 
riation. 

<Z2<J 
dt* 

rf><5 
di? 

Proper  motion 
in  S. 

o   /    // 

II 

// 

it 

H 

II 

it 

361 

+  24  41  17.62 

.21 

2 

4-  6.  328(5 

.0057 

4-  3348 

—   22 

—  .6515 

362 

+  19  51  03.13 

.25 

1 

+  6.8874 

.0061 

+  3555 

—   27 

—  .0344 

*363 

-f  57  46  3-2.43 

.40 

1 

4-  7.1371 

.0103 

+  1455 

—   15 

—  .0105 

364 

4-  27  41  54.06 

.09 

11 

4-  7.3094 

.  0038 

+  3247 

—   24 

—  .0144 

365 

4-  51  27  51.  12 

.12 

7 

+  7.5195 

.0033 

+  2024 

—   14 

4-  .  1245 

366 

+  34  11  17.40 

.17 

3 

4-  7.1381 

.0068 

+  3001 

—   21 

—  .0043 

3G7 

—  7  18  13.08 

.10 

9 

+  7.  6886 

.0044 

4-  4317 

—   52 

4-  .  0008 

•308 

-f  43  25  38.  V  3 

-j-  7.  9023 

+  2526 

—   17 

4-  .  0-21 

369 

+  49  55  56.07 

.11 

8 

+  8.  1709 

.0034 

4-  2122 

—   16 

-f-  .  2475 

"370 

-f-  54  40  52.85 

.35 

1 

+  8.  3070 

.017 

+  1783 

—   15 

4-  .160 

371 

+  25  28  26.27 

.19 

2 

+  8.3641 

.0057 

4-  3269 

—   29 

+  .0065 

37-2 

4-  10  18  36.31 

.06 

25 

4-  8.  4920 

.0021 

+  3732 

—   41 

—  .0084 

»373 

-j-  57  43  08.02 

.28 

1 

+  8.4776 

.0  06 

4-  1545 

—   17 

—  .0617 

374 

-j-  44  49  35.66 

.  12 

6 

+  8.  5908 

.0044 

4-  2444 

—   18 

+  .  0308 

375 

+  8  32  22.75 

'.06 

27 

+  9.2151 

.0020 

4-  3841 

—   46 

4-  .  3701 

•376 

+  40  1G  56.  92 

.41 

1 

+  8.9377 

.  0132 

+  2647 

—   21 

—  .  0365 

*377 

+  47  36  34.95 

.24 

2 

+  9.1196 

.0095 

4-  2256 

—   18 

—  .0188 

378 

4-  69  56  58.38 

.12 

7 

+  9.  1772 

.0041 

-  245 

—   56 

4-  .0271 

379 

4-  6  05  45.45 

.06 

24 

+  8.  7049 

.  0021 

4-  3783 

-   46 

—  .4909 

380 

+  88  55  51.  48 

.06 

22 

4-  9.2170 

.0026 

—78715 

—56385 

+  .0116 

381 

4-  52  06  28.04 

.13 

5 

4-  9.  4175 

.0047 

4-  1955 

—   17 

—  .0281 

•382 

4-  50  34  02.  65 

.56 



+  9.  5436 

.015 

4-  2066 

—   18 

+  .  026 

383 

4-  27  24  32.89 

.24 

2 

4-  9.  7185 

.0067 

-j-  3110 

—   33 

—  .0004 

384 

4-  6  55  35.57 

.15 

4 

4-  9.  8854 

.0064 

-f  3684 

—   51 

4-  .  007(1 

•385 

4-  3G  28  21.23 

.22 

2 

4-  10.3933 

.0067 

+  2733 

—   28 

4-  .  0057 

*3S6 

4-  61  42  01.60 

.26 

1 

+  10.8185 

.0076 

4-  1196 

—   24 

4-  .  0779 

387 

+  46  21  46.84 

.12 

7 

4-  10.7554 

.0042 

+  2279 

—   22 

+  .  0027 

388 

—  12  55  50.  43 

.07 

19 

+  10.8577 

.  0025 

4-  4039 

—   77 

4-  .  0003 

389 

+  77  20  02.  43 

.10 

9 

4-  11.0284 

.0038 

—  2360 

—  220 

4.  .0283 

390 

—  57  07  59.  13 

.24 

2 

4-  11.1055 

.0100 

4-  5741 

—  212 

—  .0902 

*391 

+  61  51  39.15 

.37 

1 

+  11.3494 

.0094 

4-  1166 

—   24 

4-  .  0251 

39-2 

+  39  51  26.82 

.09 

12 

4-  11.3333 

.0026 

+  2539 

—   28 

—  .0069 

393 

—  18  37  11.65 

.  11 

7 

4-  11.4971 

.0041 

+  4060 

—   89 

—  .0173 

394 

4-  38  01  50.23 

.18 

3 

4-  11.6583 

.0070 

+  2576 

—   30 

—  .0541 

*395 

+  36  02  18.  19 

.19 

2 

+  11.8195 

.0072 

+  2642 

—   32 

—  .0086 

396 

4-  10  52  47.17 

.08 

15 

4-  11.9939 

.0024 

4-  3294 

—   56 

—  .0219 

397 

4-  62  34  27.  40 

.12 

6 

4-  12.0075 

.  0038 

+  1138 

—   25 

—  .0251 

•398 

-j-  42  46  00.62 

4-  12.  1784 

4-  2374 

—   28 

4-  .  073 

399 

4-  7-2  06  28.  99 

.15 

4 

+  12.2255 

.0060 

—  '299 

—   77 

—  .  0196 

400 

H-  14  09  41.07 

.22 

2 

-f  12.2709 

.0064 

+  3187 

—   55 

—  .0541 

401 

+  20  45  48.  44 

.27 

1 

+  12.3925 

.0078 

+  3015 

—   49 

—  .0188 

402 

4-  15  28  20.30 

.10 

8 

4-  12.4808 

.0042 

4-  3138 

—   54 

4-  .  0082 

*403 

4-  55  33  52.71 

4-  12.5450 

4-  1711 

22 

—  .060 

404 

+  44  50  03:97 

.06 

24 

4-  12.6916 

.  0020 

4-  2253 

—   28 

—  .0084 

405 

4-  14  37  37.87 

.22 

9 

4-  12.6675 

.0000 

+  3098 

—   54 

—  .0631 

G10 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[204] 


Catalogue  of  500  stars 


Number. 

| 

3 

a 
dj 
«i 
« 

Name. 

Magnitude. 

Approximate 
right  ascen- 
sion, 1875.0. 

• 

l«s 

>  a 

~*  a 

3.2 
o-S 
q 
<! 

<Pa 
M* 

Ad 

w 

406 

7200 

4 

A.  m.    s. 
20  40  51.6 

8. 

4-  2.783 

s. 
Q 

// 
—  .30 

II 

—1.40 

407 

7204 

e    Cygni  .  ...... 

3 

41  09.2 

4-  2.426 

+      3 

4-1.  32 

—2  09 

408 

7206 

13  Delphini  

5.5 

41  37.0 

4-  2.975 

—      3 

—  .02 

—  .84 

*409 

7215 

5 

42  14.8 

-i-  1.489 

—      4 

4-  .06 

4-1.  39 

410 

7220 

3.5 

42  44.  7 

+  1.230 

—    14 

4-  .02 

4-1.29 

411 

7239 

fi    Aquarii  ...  

4.5 

45  54.  6 

4-  3.240 

—      8 

—  1.56 

—2  33 

*412 

7277 

v    Cvffni  .. 

4 

52  30.8 

4-  2.234 

+      4 

4-  .09 

4-  .77 

413 

7299 

5 

53  11.6 

—  2.  504 

—  309 

4-  .22 

4-1.  35 

*414 

7320 

6.5 

58  13.9 

4-  2.323 

4-      4 

—  .39 

—    9!i 

415 

7333 

£    Cygni.. 

4 

21  00  23.  1 

4-  2.  180 

+      •* 

—  .10 

—   IK; 

416 

7336 

61'Cvgni  

5  5 

01  17.8 

4-  2.68H 

+     15 

4-  .53 

—     54 

*417 

(Fed.  3689) 

01  33  6 

4-   1  462 

—      6 

4-    29 

4-2  10 

*418 

7345 

63  Cvgni 

5 

02  17  9 

-f-  2  0(i4 

_L       4 

15 

2  44 

419 

7368 

C    Cvcni  . 

3 

07  37  0 

4-  2  550- 

_L      4 

77 

—  1   l:i 

"420 

7377 

5 

08  37.2 

+  1.530 

—       4 

4-  .09 

4-  .82 

421 

7380 

a    Eqnuleii  ,.         . 

4  5 

21  09  34  5 

+  3  001 

_      3 

4-    07 

0° 

422 

7385 

5 

09  48  1 

+  2  391 

4-      4 

52 

2  (irt 

*423 

7398 

4  5 

12  30  4 

4-  2  353 

_L      5 

_|_    (jo 

4-2  13 

424 

7399 

ti    Cygni  

4.5 

12  46.  7 

+  2.463 

+      5 

—  .07 

—  .88 

"425 

7410 

a    Cephei  

3 

15  35.7 

-f  1.437 

+  .40 

4-1  58 

426 

7418 

1    Pegasi  

4 

16  18.4 

+  2.774 

+      2 

4-  .02 

—  .39 

*427 

7448 

6 

19  46  9 

4-  2  006 

-j_      5 

1  24 

—  3  37 

•428 

7453 

C9  Cygni  

6.5 

20  40.6 

+  2.445 

4-      6 

4-  .28 

4-  .04 

429 

7484 

7 

23  30  0 

—  4  602 

844 

4-     17 

-L     17 

*430 

7480 

71  Cygni  

5 

24  50.2 

4-  2.209 

+      6 

4-  .04 

—  .36 

431 

7478 

/}    Aqaarii  

3 

24  58.7 

+  3.  164 

—      7 

4-  .01 

—    45 

43-2 

7493 

8    Cephei  

3 

27  02.4 

4-  0.799 

—    34 

4-  .30 

4-1  23 

*433 

7489 

6 

27  15.5 

+  2.017 

4-      5 

4-1.57 

4-6  10 

*434 

7505 

72  Cygni  

5.5 

29  40.3 

+  2.446 

4-      7 

—  .39 

—     06 

435 

7514 

f    Aquarii..  

5 

31  05.8 

4-  3.  198 

—      8 

—  .92 

—  1  83 

436 

7521 

74  Cygni  ....... 

6 

31  56  4 

4-  2  400 

-L         7 

51 

1  02 

437 

0554 

76  Cyerni  .  . 

0 

36  32  7 

4-  2  408 

4-      8 

18 

—  3  88 

438 

7561 

2  5 

38  02  8 

+  2  948 

1 

13 

58 

*439 

7566 

79  Cvcni  .  . 

i; 

38  15  4 

4-  2  473 

4-      4 

I  07 

3  50 

440 

7571 

4 

38  59  1 

+  2  711 

-4-       5 

63 

—  2  87 

441 

7588 

11  Cephei  

4  5 

40  05  1 

4-  0  903 

—    33 

4-    43 

4-1  65 

•442 

7595 

v    Cephei  ........ 

4  5 

41  50  6 

4-  1  730 

4-       2 

-f  .09 

4-     65 

"443 

7605 

12  Cephei  

(i 

43  44  o 

4-  1  766 

4-       3 

+     52 

4-1  40 

444 

7618 

ft    Capricorni.  . 

5 

46  28  7 

4-  3  279 

11 

1  03 

—  3  33 

•445 

7627 

16  Pegasi  

5  5 

47  22  5 

4-  2  727 

4-      5 

—    21 

—    51 

*446 

7636 

6 

48  54  4 

4-  2  014 

4-       8 

4-     64 

4-"  17 

447 

7654 

79  Draconis  

6 

51  18  7 

4-  0  73(i 

—    46 

4-     69 

+4  02 

•448 

7686 

16  Cephei  

5 

57  27  5 

4-  0  882 

—    37 

—    21 

—    95 

•449 

7679 

0 

57  36  6 

+  2  458 

4-     10 

4-1  l(i 

4-'i  CO 

450 

7688 

3 

59  21  8 

-J.  3  083 

4 

04 

-     01 

[205]  CATALOGUE  OF  500  STARS. 

for  the  epoch  1875.0 — Continued. 


Gil 


Number. 

Declination,  1875.0. 

Probable  error 

of  f,  1875. 

•tl 

J3 
.U* 

"5 

£ 

IS 

i 

"3  _- 

c  3 
a  9 
< 

Probable  error 
of  annual  va- 
riation.. 

M 

» 

cPi 

dt:l 

Proper  motion 
in  (!. 

o   /    // 

// 

11 

n 

It 

// 

n 

406 

+  15  40  29.78 

.12 

7 

+  12.7372 

.0044 

4-  3040 

—   55 

—  .2110 

407 

+  33  30  10.44 

.09 

10 

-f  13.2739 

.0035 

-f  2674 

—   43 

+  .  3061 

408 

•f  5  33  00.58 

.33 

1 

+  12.9902 

.  0085 

+  3250 

—   67 

—  .  0084 

"409 

+  57  07  54.11 

.30 

1 

-f-  12.8095 

.0087 

4-  1581 

—   21 

—  .2311 

410 

+  61  21  13.39 

.12 

7 

+  13.8896 

.  0033 

4-  1319 

—   29 

+  .  8159 

411 

—  9  27  03.64 

.10 

10 

+  13.2392 

.0040 

+  3484 

—   86 

—  .0433 

*412 

+  40  41  12.20 

.12 

6 

+  13.6915 

.0040 

+  2318 

—   34 

—  .  0183 

413 

+  80  04  50.31 

.14 

4 

+  13.7227 

.0048 

—  2729 

—  371 

—  .  0305 

*414 

-)-  38  09  50.69 

.24 

2 

+  14.0641 

.0092 

+  2354 

—   38 

—  .  0066 

415 

+  43  25  47.90 

.14 

5 

+  14.2037 

.0041 

+  2184 

—   33 

—  .0006 

416 

+  39  08  08.47 

.07 

17 

-f  17.4880 

.  0028 

+  2901 

—   37 

+  3.2276 

"417 

4-  59  45  31.97 

-j-  14.2617 

4-  1436 

—   23 

—   015 

'418 

+  47  08  48!  05 

".'23' 

""2 

+  14.  3000 

.0057 

+  2045 

—   30 

—  !0154 

419 

+  29  42  54.22 

.07 

18 

+  14.5765 

.  003.J 

+  2477' 

—   49 

—  .  0673 

*420 

+  59  28  22.71 

.29 

1 

-f  14.6950 

.  C079 

4-  1454 

—   23 

—  .0088 

421 

+  4  43  55.81 

.14 

4 

+  14.6732 

.0048 

+  2902 

—   76 

—  .0872 

422 

-j-  37  30  45.48 

.14 

4 

-(-  15.2070 

.0044 

+  2308 

—   43 

+  .  4332 

M23 

+  38  52  17.47 

.13 

5 

4-  14.9311 

.0043 

-f  2226 

—   41 

—  .0017 

424 

+  34  22  22.33 

.28 

1 

4-  14.9299 

.0066 

4-  2330 

—   45 

—  .  0188 

•425 

+  62  03  23.00 

.07 

21 

+  15.1537 

.0022 

+  1334 

—   24 

+  .  0418 

426 

+  19  16  14.37 

.12 

6 

+  15.2039 

.0040 

+  2593 

—   62 

+  .0511 

•427 

+  51  07  11.76 

.28 

1 

+  15.3164 

.0101 

+  1816 

—   30 

—  .  0337 

•428 

-f  36  07  41.23 

.25 

1 

+  15.3758 

.  0067 

4-  2220 

—   45 

—  .0246 

42'J 

+  83  43  44.24 

.30 

1 

+  15.5592 

.0111 

—  4299 

—  947 

+  .  0017 

*430 

+  45  59  24.26 

.19 

3 

-f-  15.7294 

.0052 

-f  1953 

—   36 

4-  .  0984 

431 

—  6  07  12.05 

.06 

24 

+  15.6223 

.0028 

4-  2823 

—   92 

—  .0165 

432 

-f  70  00  43.  81 

.07 

21 

4-  15.7464 

.0022 

4-  655 

—   37 

—  .  0047 

"433 

-j-  52  04  09.  09 

4-  15.  81X9 

4-  1746 

—   30 

+  .  051 

*434 

4-  37  58  27.35 

.14 

5 

+  15.9709 

".'6644' 

+  2116 

—   46 

+  .0844 

4-5 

—  8  24  49.39 

.10 

9 

4-  15.9330 

.0041 

4-  2758 

—   96 

—  .  0353 

436 

-f-  39  51  09.77 

.24 

2 

4-  16.0117 

.0059 

+  2039 

—   44 

—  .0002 

437 

+  40  14  16.92 

.33 

1 

+  16.1694 

.0084 

+  1987 

—   45 

—  .  0828 

438 

+  9  18  10.14 

.07 

19 

+  16.3231 

.0031 

-f  2428 

—   78 

—  .  0058 

*439 

+  37  42  42.66 

.55 

...... 

+  16.3075 

.019 

+  2021 

—   51 

—  .  032 

440 

-j-  25  04  16.37 

.19 

3 

+  16.3657 

.0054 

-f-  2212 

—   62 

—  .0107 

441 

+  70  44  10.05 

.12 

6 

+  16.5i83 

.  0052 

+  709 

—   35 

+  .  0965 

*442 

+  60  32  39.77 

.11 

8 

4,  16.5080 

.  0034 

4-  1:559 

—   26 

—  .0115 

"443 

+  60  06  46.94 

.30 

1 

4-  16.6117 

.0079 

+  1374 

—   26 

—  .0010 

444 

—  14  08  21.03 

.11 

8 

+  16.7437 

.0040 

+  2576 

—  107 

—  .0023 

*445 

+  25  20  15.72 

.08 

13 

4-  16.7709 

.0049 

+  2102 

—   64 

—  .0121 

*446 

-f-  55  37  25.52 

.24 

2 

4-  16.8636 

.0063 

+  1518 

—   31 

+  .0017 

447 

+  73  06  39.91 

.12 

6 

4-  17.0061 

.0061 

+  505 

—   41 

+  .0312 

"448 

+  72  35  06.  16 

.16 

4 

4-  17.0786 

.0050 

+  568 

—   35 

—  .1765 

•449 

-j-  42  12  42.70 

4-  17.2950 

4-  1748 

—   49 

+  .  033 

450 

—  0  55  34.69 

.06 

28 

+  17.3257 

.0020 

+  2185 

—   92 

—  .  0139 

612 


UNITED  STATES  NORTHERN  BOUNDARY  COMMISSION. 


[200] 


Catalogue  of  500  stars 


Number. 

I 

3 

a   .' 
dj 
-4 

a 

Name. 

Magnitude. 

Approximate 
right  ascen- 
sion, 1875.0. 

Annnal  varia- 
tion in  a. 

<?2,2 
(fa4 

Ac! 

A// 

451 

7C8D 

v    Pe^asi  .......  . 

5 

/i.   m.     s. 
21  59  22  5 

s. 
+  3  028 

8. 
0 

// 
43 

it 

S" 

452 

7692 

2 

22  00  20  7 

-f-  3  810 

40 

•57 

J     0.1 

453 

7706 

i     Peuasi  . 

4 

01  11  6 

+  2  789 

_i_      n 

4-      11 

1  41 

454 

7733 

6 

04  35  8 

+  2  832 

-L        r, 

+     30 

1  r)'t 

455 

7749 

4 

06  ul  2 

_j_  2  073 

-t-     11 

.     01 

O'i 

*45(i 

7755 

5.5 

07  16  3 

+  2  036 

4-    11 

11 

00 

'457 

7765 

5 

08  30  9 

+  2  568 

-(-     11 

+     40 

+1  48 

458 

7773 

4.5 

10  14  2 

-f  3  170 

g 

74 

1  'J8 

"459 

7787 

6 

13  48  4 

-f-  2  310 

-4-     14 

4-     7H 

4-'>  HO 

400 

7795 

y    Aquarii  ....   .  .  

•    3 

15  12  0 

+  3  102 

4 

Q." 

-i       0^ 

*461 

7800 

2    Lacerta}     .  ......... 

5 

15  P2  0 

+  2  468 

4-      14 

''3 

0° 

462 

7814 

TT   Aquarii     .  .... 

5 

18  53  6 

+  3  065 

•j 

17 

7<i 

*403 

7H20 

4      1  ;icri'l;i>    ..    .   ...    .. 

5 

19  27  0 

-f-  2  419 

J-     1ri 

54 

7-1 

464 

7843 

38  Pegasi  . 

6 

24  18  9 

4-  2  738 

-I-     1  1 

00 

F9 

4(35 

7848 

61   Cephei 

4  5 

24  31  9 

+  2  215 

4-     17 

+    56 

4-"  01 

466 

7855 

a     Lacertae.  

4 

26  OS.  6 

-)-  2.  4">9 

4.     17 

+    05 

+    55 

467 

7868 

17    Aqnarii  

4 

28  56.0 

-f  3  084 

•» 

4-1   "8 

468 

7881 

5  5 

30  04  4 

_|_  i  082 

'!'! 

-I      59 

4-      1  1 

*469 

7882 

6 

30  42  0 

+  2  479 

-4-     17 

07 

i  i    40 

*470 

7907 

6 

34  31  9 

-)-  1  301 

18 

4-    7fi 

•  1  'i  80 

471 

7908 

f    Pegasi  

3 

35  13.6 

-f  2  988 

4.       2 

00 

+1   63 

472 

7923 

TI    Pegasi  

3 

37  08.7 

+  2  K)4 

4.     11 

30 

1   18 

*473 

7945 

A    Perils!  .. 

4  5 

40  30  6 

+  2  883 

4-        H 

11 

Ori 

474 

7958 

ft    Pegasi  

4 

43  58.3 

-f  2  888 

_L      9 

0'? 

4-     07 

*475 

7962 

14  LacertcB   . 

e 

44  43  7 

_j_  2  694 

-)-      17 

4-      1S 

5° 

476 

7967 

(     Cepbei  

4 

45  14.0 

-)-  2  119 

4-    22 

+    26 

4-     30 

477 

7970 

A    Aquarii  

4 

40  05.5 

-f-  3  131 

0 

99 

1  73 

478 

7992 

a,    Piscis  Australis  ...... 

1 

50  44.  3 

-J-  3  327 

21 

28 

4-    ()2 

479 

8023 

o    Andromeda}  

4 

5(5  10.4 

+  2  747 

4-     ll> 

04 

;»  (J4 

*480 

8024 

6  5 

56  14  0 

+  2  519 

4-     '2fi 

10 

1  31 

481 

8032 

2 

57  43  1 

+  2  904 

4-     12 

-    ^fi 

1   47 

482 

8034 

a    Pegasi  .  ... 

2 

58  32  1 

+  2  984 

4-       fi 

"3 

1  81 

•483 

8036 

3    AudromedjB  ......... 

5  5 

58  34  5 

_|_  g  (576 

4-     2'i 

.    _        0.1 

+    ri 

*484 

8059 

5    Andromeda)  .  ..... 

6 

23  02  01  9 

+  2  708 

+     24 

+      01 

_L      Ql 

»4tf5 

8083 

6 

07  16  2 

+  2  8U1 

.     37 

00 

i      09 

486 

8124 

5.5 

13  30  1 

-f  2  438 

+     41 

+1  61 

+3  6° 

•487 

8128 

6 

13  55  7 

-f-  2  842 

+        01 

4K 

i  (ir* 

483 

8177 

6    Pieoium...  .  

5 

21  37  6 

+  3  041 

4-       3 

1  64 

3  O'l 

"483 

8206 

72  Pegasi  

5.5 

27  45  1 

+  2  9(i3 

4-     16 

"1 

53 

490 

8224 

A    Andromeda)  .  .  

4.5 

31  27  1 

+  2  917 

4-     28 

4-     02 

00 

491 

8229 

(     Andromedss  

4 

23  32  00  6 

+  2  923 

4-     25 

4-     2R 

1  70 

492 

8233 

i     Pisciuui 

4  5 

33  31  4 

+  3  085 

3 

.     10 

_i_i   i  -j 

493 

8238 

y    Cepliei  

3 

34  13  * 

-f  2  405 

4-     73 

4-     4° 

-j-1  15 

494 

8237 

K    Andromeda?  

4.5 

34  15  4 

-f  2  937 

4-     26 

4-     47 

11 

*495 

8273 

5 

41  56  6 

-f-  2  8''3 

60 

-      Q«> 

-   i  *m 

[207]  CATALOGUE  OF  500  STAES. 

for  the  epoch  1875.0 — Continued. 


613 


Number. 

Declination,  1875.0. 

Probable  error 
of  6,  1875. 

4J 

1 

<D 

* 

Annnal  varia- 
tion, 1875.0. 

Probable  error 
of  annual  va- 
riation. 

<P<5 
P 

<r><j 

dt3 

Proper  motion 
in  i. 

o   /    // 

II 

u 

// 

// 

n 

n 

451 

+  4  26  54.27 

.24 

2 

+  17.4299 

.0070 

4-  2150 

—   87 

+  .  0898 

452 

—  47  33  54.  17 

.22 

2 

+  17.2104 

.  0094 

4-  2703 

—  169 

—  .0282 

453 

4-  24  44  06.85 

.13 

6 

4-  17.4253 

.0043 

4-  1955 

—   69 

4-  .  0059 

454 

4-  20  21  51.76 

.25 

1 

4-  17.5392 

.  0070 

4-  1916 

—   73 

—  .0259 

455 

-j-  57  i5  07.92 

.10 

9 

4-  17.6493 

.0032 

4-  1361 

—   34 

4  .  0037 

*456 

4  58  47  53.44 

.25 

1 

4-  17.6458 

.0072 

4-  1330 

—   33 

—  .0310 

*457 

4-  39  05  43.24 

.20 

2 

4-  17.7168 

.0059 

4-  1672 

—   56 

—  .0112 

458 

—  8  24  17.80 

.08 

15 

4-  17.7731 

.0035 

4-  2059 

—  102 

—  .0248 

•459 

4-  52  01  49.94 

4-  17.9577 

-j-  1426 

—   43 

4-  .018 

460 

—  2  00  59.24 

.09 

12 

4-  18.0066 

.0036 

4-  1925 

—   96 

4-  .0128 

*4G1 

4-  45  54  26.93 

.26 

1 

4-  18.0002 

.0071 

4-  1501 

—   51 

—  .0192 

462 

+  0  44  37.64 

.12 

6 

4-  18.  1296 

.0046 

.  4-  1831 

—   93 

—  .0046 

•403 

4-  48  50  34.  36 

.26 

1 

4-  18.1255 

.  0059 

4-  1423 

—   48 

—  .  0294 

4G4 

+  31  56  00.28 

.18 

3 

4-  18.3128 

.0069 

+  1542 

—   69 

—  .0189 

465 

-j-  57  40  33.  16 

.15 

4 

+  18.3424 

.0040 

4-  1229 

—   39 

4-  .  0031 

466 

4-  49  38  25.05 

.11 

8 

4-  18.4025 

.C035 

4-  1357 

—   51 

4-  .  0065 

467 

—  00  45  40.21 

.07 

17 

4-  18.4345 

.0036 

+  1653 

—   9!i 

—  .  0572 

468 

+  75  34  56.49 

.16 

4 

4-  18.5212 

.0061 

4-  523 

—   31 

—  .0089 

"469 

4-  49  25  26.  62 

4-  18.5690 

4-  1294 

—   52 

4-  .018 

*470 

4-  74  43  19.24 

.33 

1 

4-  18.7168 

.0111 

4-  592 

—   26 

J—     >  V  M-\J 

+  .041 

471 

+  10  10  45.77 

.07 

18 

4-  18.6852 

.0031 

+  1497 

—   89 

—  .0127 

472 

+  29  34  04.43 

.11 

7 

4-  18.7101 

.  0042 

4-  1366 

—   74 

—  .0478 

•473 

+  22  54  29.73 

.12 

6 

4-  18.8352 

.0040 

4-  1347 

—   80 

—  .0248 

474 

+  23  56  31.  11 

.12 

6 

4-  18.9105 

.0043 

4-  1294 

—   81 

—  .0503 

*475 

+  41  17  31.12 

.30 

1 

+  18.9721 

.0076 

4-  1185 

—   66 

—  .0102 

476 

4-  63  32  35.59 

.10 

9 

4-  18.8635 

.0031 

+  903 

—   35 

—  .  1330 

477 

—  8  14  39.10 

.09 

11 

4-  19.0501 

.0037 

+  1364 

—  103 

4-  .  0357 

478 

—  30  17  03.  08 

.12 

7 

4-  18.9746 

.0057 

4-  1371 

—  123 

—  .1708 

479 

+  41  39  15.78 

.12 

6 

+  19.2431 

.0043 

4-  1019 

—   70 

—  .0381 

*480 

+  56  26  02.61 

.33 

1 

4-  19.2638 

.0134 

4-  926 

—   55 

—  .0191 

481 

4-  27  24  18.34 

.12 

7 

4-  19.4466 

.0038 

+  1001 

—   83 

—  .128'} 

482 

4-  14  31  5!'.  01 

.06 

24 

4-  19.2872 

.0022 

4-  1071 

—   90 

—  .0501 

•483 

4-  49  22  22.11 

.18 

3 

4-  19.4886 

.0053 

4-  959 

—   66 

4-  .  1503 

*484 

4-  48  36  54.6-2 

.25 

1 

4-  19.5354 

.  0062 

4-  909 

—   68 

4-  .1181 

'485 

4-  56  28  41.74 

.22 

2 

+  19.7947 

.0076 

4-  919 

—   79 

4-  .  2689 

486 

4-  67  25  40.26 

.19 

6 

4-  19.6601 

.0044 

+  636 

—   51 

4-  .  0172 

*487 

4-41  23  38.04 

.23 

1 

4-  19.6509 

.0067 

+  742 

—   78 

+  .  0005 

488 

-j-  5  41  33.03 

.12 

6 

4-  19.7175 

.0039 

4-  652 

—   96 

—  .0563 

*4i-9 

4-  30  38  07.66 

.25 

1 

4-  19.8347 

.  0060 

4-  520 

—   89 

—  .0213 

4'JO 

-j-  45  43  51.87 

.19 

3 

4-  19.4689 

.0047 

4-  446 

—   85 

—  .4300 

491 

4-  42  34  34.26 

.13 

6 

4-  19.8999 

.0050 

4-  434 

—   86 

—  .0050 

492 

4-  4  56  56.19 

.07 

19 

4-  19.4773 

.0029 

4-  437 

—  102 

—   4432 

49:? 

4-  76  56  04.87 

.07 

21 

4-  20.0711 

.0022 

4-  304 

—   49 

+  .  1435 

494 

4-  43  3:!  31.  17 

.25 

2 

4-  19.9077 

.0060 

+  395 

—   87 

—  .0-201 

M95 

+  67  06  44.  16 

.16 

4 

+  19.9722 

.0051 

4-  238 

—   78 

—  .0198 

614  UNITED  STATES  NOKTHEKN  BOUNDARY  COMMISSION.         [208] 

Catalogue  of  500  stars 


a 

Igd 

a 

1 

. 

C    O  iO 

e3   a 

t4 

£ 

ojj 

Name. 

•o 
1 

«1- 

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44 

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e 

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fi-.^f  o 

c  -^ 

3 

o 

* 

« 

X 

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•3 

7t.  m.     s. 

g 

8. 

« 

„ 

*496 

8314 

5 

23  48  46.  3 

4-  2.  S50 

4-    88 

—  .25 

—  .70 

*497 

8324 

5.5 

51  23.5 

4-  3.047 

4-    15 

—  .06 

—  .  10 

498 

8331 

w    Piscium  ............. 

4.5 

52  53.  (i 

4-  3  078 

4-      5 

—1  '26 

*499 

8344 

5 

55  15.0 

4-  3.026 

4-    52 

4-  .37 

41  59 

*500 

8366 

5 

58  39.4 

4-  3.061 

4-    54 

—  .16 

+  .90 

\ 

[209J  CATALOGUE  OF  500  STARS. 

for  the  epoch  1875.0 — Continued. 


615 


Iff 

•-o 

2  i 

a 

exj 

O 

j 

Declination,  1875.0. 

•2S- 

4! 

*fe 

9   S   ,4 

W 

A) 

t      o 

1 

^  **H 

.y 

"5   - 

c  a 

=  ° 

J|| 

dij 

df 

I*  w 
<D  -~ 
PH 

3 

03 

K 

PH 

" 

DH 

PH 

O          '                " 

tl 

y/ 

it 

„ 

„ 

„ 

"496 

4-  73    42    53.04 

.13 

5 

4-  20.0211 

.0066 

+    117 

—      60 

—    .  0090 

*497 

4-  24     26     47.71 

.15 

4 

4-  19.99(50 

.  0054 

+      81 

—      98 

—    .0440 

498 

+     6    10     16.47 

.08 

16 

4-  19.9300 

.0032 

4-      53 

—    101 

—    .1146 

•499 

-j-  60    31     35.85 

.25 

1 

4-  20.0299 

.  0077 

+        5 

—      95 

—    .0201 

"500 

-f  60    37    04.34 

.47 

4-  20.0599 

.016 

—      60 

—      99 

+     .006 

SPECIAL  INDEX  TO  APPENDIX  H. 


Page. 

ABO  Catalogue 5,6,7,15,21,78,103 

AIRY,  Sir  G.  B.  (See  Cambridge  and  Green- 
wich)   17,21,23,24,25,35,36 

AMERICAN  EPHEMERIS 5, 8, 9 

APPROXIMATE  positions  of  stars 9 

ARGELANDER  (See  Abo,  Bonn,  etc. ) 4, 28, 144 

ARMAGH  17,39,113 

ASSUMED  POSITIONS  for  1875.0 9 

ASTRONOMICAL  Soc.  CAT 20,23 

AUTHORITIES,  Enumeration  of 14 

— ,Nomenclature  of 14 

— ,  Selection  of 14 

AUWERS,  ARTHUR 5, 21, 22, 28, 33, 71, 78, 81 

BACKHUYZEN,  VANDE  SANDE 36 

BAILY 6 

BERLIN  JAHRBUCH  43 

BESSEL  (See  Kon.  Beob.,  Fund.  Astr.,  etc.)..          5 
BESSEL'S REFRACTIONS  (See  Refractions). .  .21, 22, 67 

BLACKHEATH 6,17,21,99 

BONN  BEOB. 

— ,  Vol.  VI 18,43,143 

— ,Vol.  VII 4 

BRADLEY.     (See  Fund.  Ast.) 

BRINKLEY  5 

BRITISH  Ass.  CAT 27 

BRUHNS,  C.  (Sec  Leipzig) 6,10,21 

BRUSSELS  Obs . ._. 17, 42, 130, 136, 141 

BUSCH.     (See  Kim.  Beob.) 

CALLET'S  refractions 41 

CAMBRIDGE  Obs 15, 16, 18, 23, 79, 107, 112, 131 

CAPE  OF  GOOD  HOPE  Obs. : 

— ,  Fallows,  1831 17,22,105 

— ,  Henderson,  1833 15,22,79,106 

— .Stone,  1860 10,16,42,81,133 

CATALOGUE,  Wu  68 62 

—  final,  of  500  stars 186 

CHALLIS.     (See  Cambridge.) 

CHRISTIE,  W.  M 35 

CONTENTS 7 


Page. 

CORRECTIONS,  preliminary 19 

—  to  assumed  declinations : 

First  approximation  (Table  III) 82 

Second  approximation  (Table  V) 91 

First  approximation  for  stars  — 30°  to 

—90°  (Table  VII) 95 

—  SYSTEMATIC,  Tables  of: 

First  approximation  (Table  II) 76 

For  Fund.  Astr.,  final 89,90 

Tables  IX  and  X 154 

Table  XII. 168 

Recapitulation  of 173 

CORRECTION,  Probable  common,  to  nortbeni 

boundary  field  catalogue  (section  X) 169 

CURVES.     (See  graphic  curves.) 

D'AGELET.     (See  Gould.) 

DAVIS,  ADMIRAL,  C.  H 5 

DEFINITIVE  corrections.    (See  Corrections.) 
DISCORDANCE  of  reflection  obs.     (See  reflec- 
tion obs. ) 
DIVISION  ERROR: 

Cape  circle — .  23 

Edinburgh  circle 28 

Greenwich  transit  circle 34, 35 

Washington,  Mural  circle 40 

Washington,  Transit  circle 44 

Paris,  Mural  circle 41 

Leiden,  Transit  circle 44 

DOLLEN 14,21 

DOOLITTLE,  PROF.  C.  L 5 

DORPAT  Obs 7, 15, 17, 20, 21, 78, 101 

DUDLEY  OBSERVATORY 3, 4, 5 

EASTMAN,  Professor  (See  Washington  Obs. ) . .  5, 16 
EDINBURGH  Obs. . .  .15, 18, 27, 28, 33, 79, 109, 116, 167 

— ,  Special  discussion  of  Eh  43 28 

— ,  Special  table  of  corrections  to  Eh  43 32 

ELLERY,  R.  L.  J.    (See  Melbourne.) 
ENGLEMANN.     (See  Leipzig.) 

617 


618 


SPECIAL  INDEX  TO  APPENDIX  H. 


[212] 


EPIIEMERIS.    (See  Am.  Eph.  Naut,  Aim.  etc.) 
EXPLANATION  of  tables... 


Pago. 


170 


FALLOWS.    (See  Cape  of  Good  Hope  Obs.) 

FAYE 36,54 

FEATHERSTONHAUGH,  T.  B 5 

FLEXURE,  Cambridge 24 

— ,  Cape 42 

— ,  Greenwich 35 

— ,  Melbourne 43 

— ,Eadcliffe 39 

—.Paris 41,42 

— .Poulkowa 79,118 

— ,  Washington  Transit  circle 44, 50, 54 

FUND  AMENTA  ASTRONOMIC 5,  G,  17, 20, 36, 82 

— ,  discussion  of  syst.  corr 82 

— ,  definitive  tables  of  syst.  corr 89, 90 

GILLIS.    (See  Washington  and  Santiago.) 

GOULD, Dr.  B.  A 5,9,13,81 

GRAPHIC  CURVES,  remarks  on 94 

GREENWICH  OBSERVATIONS 33 

— ,  Bradley  (See  Fund.  Astr.). 

— ,Pond 5,15,17,21,22,78,101,104 

— ,  Twelve-year  (1840 and  1845) ...  15, 34, 79,  111,  117 

— ,  Six-year  (1850) 16,34,81,123 

— ,first  Seven-year  (1860) 16,34,81,132 

— ,  New  Seven-year  (1864) 16, 34, 81, 139 

— ,  recent  annual  results 16, 34, 81, 144, 150 

— ,  recent,  special  remarks  on 34, 81, 144 

GROOMBRIDGE.    (SceBlackheath.) 

GYLDEN,  HUGO.    (See  Poulkowa) . .  43, 133, 137, 148 

HALL,  Professor  (See  Washington  Obs. ) 16, 40 

HARKNESS,  Professor  (See  Washington  Obs. ) .          5 
HENDERSON.     (See  Cape  of  Good  Hope  and 
Edinburgh. ) 

HILL.G.W: 10 


IVORY'S  refractions 27 

• 

JOHNSON.    (See  St.  Helena.) 

KAISER.    (See  Leiden.) 
KONIGSBERG  Beob. 

Bessel,  1821 6,14,21,78,100 

Bessel  and  Busch,  1838 15, 79, 110 

—  Bessel  and  Luther,  1843 15, 33, 79, 115 

LALANDE 18 

LATITUDE,  of  Cambridge 25,26 

— ,  of  Edinburgh 31 

— ,  of  Greenwich 36 

— ,  of  Eadclifie 39 

— ,  of  Washington 40, 41, 59 

— ,  secular  variation  of 26, 37, 60 


Pago. 
LAMONT.    (See  Munich  Obs.) 

LAUGIER  (See  Paris  Obs. ) 6, 16 

LEIDEN  Obs 7,16,43,81,147 

LEIPZIG  Obs 18,43,146 

LITTROW.    (See  Vienna.) 
LUTHER.     (See  Kon.  Beob.) 

MIDLER 5 

MADRAS  Obs 18,26,164,166 

MAIN,  EEV.  EGBERT.    (SeeEadcliffe.) 

MARTH,  A 33 

MELBOURNE  Obs 7, 10, 16, 18, 42, 81, 137, 148 

— Comparison  with  Wn  G8 66 

MOSTA.    (See  Santiago). 

MUNICH  Obs 17,23,108 

NAUTICAL  ALMANAC,  Brit 23, 26, 27, 42 

NEWCOMB, Prof.  S.  (See  Washington  Obs.). 4, 9,21, 

35,41,44 

NOMENCLATURE  of  authorities 14 

NORMAL  SYSTEM,  first  approximation  to 71 

NOTATION  in  discussion  of  Wn  68 45 

NOURSE,  Professor 5 

NUTATION,  values  of 19 

NYREN,  Dr.  Magnus 26 

OLUFSEN.    (-See  Greenwich,  Pond.) 

OOM.F.  A 18,113 

PALERMO,  catalogue 6, 17, 21, 97, 164 

PARIS  Observations 17, 18, 41, 128, 135, 140, 142 

— ,  Laugier's  catalogue 16, 41, 81, 125 

PETERS,  DR.  C.  A.  F.  (-See  Poulkowa) 10, 19 

PIAZZI.     (See  Palermo.) 

POND.    (See  Greenwich.) 

POSITIONES  MED.,  Struve.     (SeeDorpat.) 

POULKOWA  Observations 18, 19, 167 

— ,  catalogue  for  1845 15, 39, 79, 118 

PRECESSION  terms,  computation  of. 10, 13 

—.formulae 11,13 

— Coefficients 11 

— ,  of  stars  within  10°  of  pole 14 

PROBABLE     ERROR,    frequently     discussed 

throughout  the  work 

PROPER  MOTION,  frequent  allusions  to 

— ,  influence  on  precession 10,11 

— ,  values  of,  in  declination    (Seecatalogue.) 

QUETELET.    (See  Brussels  Obs.) 

BADCLIFFE  Obs. : 

for  1845 15,21,37,79,120 

for  1845,  special  comparison  with  Eh  45 

and  Pa  45 79 

for  1860 : 18,37,134 


[213] 


SPECIAL  INDEX,  TO  APPENDIX  H. 


619 


Pago. 
RADCLIFFE  Obs.— Continued. 

annual  results 16, 37, 81, 145, 151 

special  table  of  corrections 

remarks  on « ^  I 

REFLECTION  OBSERVATIONS  : 

at  Cambridge    24,25 

at  Greenwich 

at  Radcliffe 

at  Washington 44,50,54 

REFRACTION  .... 22, 27, 34, 37, 41, 42, 43, 59, 66, 68, 88 
ROBINSON.    (See  Armagh.) 

SAINT  HELENA,  catalogue 15, 22, 78, 105 

SAFFORD,  Prof.  T.  H 

SANDS,  Admiral  B.  F 

SANTIAGO  Obs.,  Gillis,  1851 17,41,124 

-,  Mosta,  1855 16,41,81,126 

SMYTH,  Prof.  Piazzi.    (See Edinburgh  Obs.) 

STARS,  Selection  of,  to  form  catalogue 

STONE,  E.  J.     (See  Greenwich  and  Cape  of 

Good  Hope) 34,42,43,66 

STRUVE,  O.    (See  Poulkowa.) 
STRUVE,  W.     (SeeDorpat.) 
SYSTEMATIC  CORRECTIONS  in  declination : 

— ,  Special  table  for  Eh  43 32 

— , Wn68 Cl 

— , Wn68andMe68 68 

— ,  Table  II,  first  approximation 76 

— ,  definitive  determination  of 93-169 

— ,  depending  on  A.  R.,  remarks  on 94,96 

— ,  to  declinations  from— 30°  to— 90° 94 

— ,  Table  VI,  preliminary 95 

— ,  definitive,  Table IX,  order  of  declination..       154 

— ,— ,  Table  X,  order  of  A.  R 159 

,  Table  XII 168 

— ,  recapitulation  of 173 


TAYLOR,  T.  G.    (See  Madras.) 
VIENNA  Obs 


Page. 
.17,21,102 


WASHINGTON  OBSERVATIONS 7,9,68,81 

,  Mural  Circle ...  15, 16, 19, 40, 81, 121, 127, 138, 167 

— ,  Prime  Vertical  Transit ...18,166 

— ,  Transit  Circle,  1865-1869,  Special  discus- 
sion of 

— , catalogue  of  Wn  68 62 

— , comparison  with  Me  68 66 

— ; description  of  observations 44 

— , discordance  "R-D" 50 

— , ,  table  of,  for  Wn  67 52 

— , Wn68 54 

— , latitude 59 

— j ,  secular  variation  of 60 

— ; nadirs  in  1867,  correction  of 46 

— , notation 45 

— , probable  error 48 

_ refraction 59,66,81 

— , systematic  corrections 61, 68 

— , weights,  table  of 53 

— , zenith  points  for  1868 47 

— ,  results  for  1868-1869 81,149 

— ,  results  for  1870-1874 68, 70, 81, 152 

— ,  special  table  of  corrections  to  ass'd  <5 69 

WEIGHTS,  preliminary,  for  normal  system..        72 

-,  final 93,96,163 

— ,  Table  XI  (definitive) 160 

WIEN.    (See  Vienna.)    • 

WILSON,  O.  S 5 

WOLFERS,  Tabulae  Reductionum 5,144 

YARNALL,  Prof.  M.     (See  Washington,  Mural 

Circle) 19,40 

YOUNG'S  refractions 22 


EXPLANATION. — It  has  been  found  necessary  to  omit  Part  2  of  Appendix  H,  containing  the  details 
of  corrections  to  assumed  places. 


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UNIVERSITY  OF  CALIFORNIA  LIBRARY 


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